Search results “Diagonal matrix product”

MathsResource..io | Linear Algebra | Diagonal Matrices

Views: 12921
Maths Resource

This video defines a diagonal matrix and then explains how to determine the inverse of a diagonal matrix (if possible) and how to raise a diagonal matrix to a power.
Site: mathispower4u.com
Blog: mathispower4u.wordpress.com

Views: 57739
Mathispower4u

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 10455
MathTheBeautiful

This precalculus video tutorial provides a basic introduction into multiplying matrices. It explains how to tell if you can multiply two matrices together and how to determine the order of the new matrix. The order of the new matrix is based on the rows of the first matrix and the number of columns in the second matrix. To multiply two matrices together, multiply the rows of the first matrix by the columns of the second matrix and find the sum of the products. This video contains plenty of examples and practice problems on matrix multiplication.
Precalculus New Video Playlist:
https://www.youtube.com/watch?v=DrEXTC6mIO8&list=PL0o_zxa4K1BU5sTWZ2YxFhpXwsnMfMke7
Access to Premium Videos:
https://www.patreon.com/MathScienceTutor
https://www.facebook.com/MathScienceTutoring/

Views: 31489
The Organic Chemistry Tutor

Learn via an example what is a diagonal matrix. For more videos and resources on this topic, please visit http://ma.mathforcollege.com/mainindex/01introduction/

Views: 29927
numericalmethodsguy

When you have a diagonal matrix, everything in linear algebra is easy
Learning Objectives:
1) Solve systems, compute eigenvalues, etc for Diagonal Matrices
This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati

Views: 1082
Trefor Bazett

Views: 2239
Ahmed Fathi

Introduction to Linear Algebra
Strang 4th edition
Problem 2-7-11
Which permutation makes PA upper triangular? Which permutations make PI AP2 lower triangular? Multiplying A on the right by P2 exchanges the of A.

Views: 450
Marx Academy

Setting out the steps to diagonalise a 3x3 matrix:
Finding the characteristic polynomial and solving it to find the eigenvalues.
Finding a set of linearly independent eigenvectors.
Forming the matrix and inverse matrix composed of the eigenvectors.
Pre- and post-multiplying by these matrices to obtain the diagonal matrix.

Views: 499601
DLBmaths

Every operator on a finite-dimensional complex vector space has a matrix (with respect to some basis of the vector space) that is a block diagonal matrix, with each block itself an upper-triangular matrix that contains only one eigenvalue on the diagonal.

Views: 3622
Sheldon Axler

In this presentation we shall see how to evaluate determinants using diagonal product method.

Views: 1360
Ram Polepeddi

Diagonal matrix is a type of square matrix having all the non-diagonal elements equal to 0.

Views: 3805
themathinstructor

In this video, I show you why the determinant of a diagonal matrix is simply the product of the diagonal entries.

Views: 163
Polar Pi

The determinant of an upper triangular matrix
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-simpler-4x4-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-after-row-operations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 144012
Khan Academy

Learn the definition of a diagonal and identity matrix. For more videos and resources on this topic, please visit http://nm.mathforcollege.com/topics/primer_sle.html

Views: 8606
numericalmethodsguy

Subscribe for More Lessons: https://YouTube.com/WeSolveThem
Tip for Good Service: https://PayPal.me/WeSolveThem
Thousands of free solutions: https://WeSolveThem.com
Commenting and Full Lesson Available @ http://wp.me/p7kK3u-Af via WeSolveThem.com
Lessons are always AD-FREE @ WeSolveThem.com
Description: Partitioned Matrices or Block Matrix Multiplication
Half off 12 months -- use code HALFOFFNOW @ http://wesolvethem.com/register
Copyright © 2013 → ∞ WeSolveThem.com - JJtheTutor, Inc. All rights reserved | Made By Students, For Students.

Views: 20558
JJtheTutor

3.2.3 Diagonal Matrices

Powered by Tamada Media
☛Subscribe here - https://goo.gl/wKmO6Z
☛Facebook - https://www.facebook.com/talentsprint/?fref=ts
☛Visit Our WebSite - http://www.talentsprint.com/it

Views: 15522
TalentSprint Coding Bootcamp

Lower Triangular Matrix
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Er. Ridhi Arora, Tutorials Point India Private Limited.

Views: 3023
Tutorials Point (India) Pvt. Ltd.

Types of Matrices, Square matrix, Diagonal matrix, Scalar matrix Matrices
For more Details: http://www.smartsolutionz.in/NCERT-Solutions-for-Class-12-Maths-Chapter3-Matrices.html
http://www.smartsolutionz.in/NCERT-Solutions-for-Class-12-Maths-Chapter4-Determinants.html
Easily understandable HD animated videos for CBSE Class 11 & 12 Students. NCERT solutions Maths To view all our video's please download our android app. please subscribe to watch all our video in you tube.
( app contains full HD Animated videos based on the important Topics, MCQ's for Neet, printable Notes, question bank, fully solved Example & exercise problems and much more... )
Click on the below to download our app
https://play.google.com/store/apps/details?id=com.PUSmartLearning.smartsolutions.smartsolutionz
our website: http://www.smartsolutionz.in/
for mare information call +91 7847825500
NCERT Solutions:
http://www.smartsolutionz.in/NCERT-Solutions.html
NCERT Syllabus:
http://smartsolutionz.in/NCERT-Syllabus.html
JEE:
http://www.smartsolutionz.in/JEE.html
our website:
http://www.smartsolutionz.in/
PUC Exam Time table:
http://www.smartsolutionz.in/PUC-Exam-Time%20table-2018.html
http://www.smartsolutionz.in/PUC.html
CET:
http://www.smartsolutionz.in/Karnataka-CET-2018.html
SSLC Exam Time table:
http://www.smartsolutionz.in/SSLC-10th-Exam-Time%20table-2018karnataka.html
https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=17&cad=rja&uact=8&ved=0ahUKEwj7sqqvqrHYAhWGuI8KHXBVB5IQFghuMBA&url=http%3A%2F%2Fwww.smartsolutionz.in%2FPUC-Exam-Time%2520table-2018.html&usg=AOvVaw1unqdUQvWdCZYQzyPTD1ot

Views: 442
PUC Karnataka

Learn the definition of an upper and lower triangular matrix. For more videos and resources on this topic, please visit http://nm.mathforcollege.com/topics/primer_sle.html

Views: 54690
numericalmethodsguy

Diagonal matrix definition 9th unit 1 (Matrices)

Views: 4557
prof. Khurram Arshad

Program to find the elements of Lower triangle, Upper triangle and Diagonal elements of given square matrix.

Views: 6499
Sundeep Saradhi Kanthety

Watch the full playlist : https://goo.gl/hiBsaO
This video lecture " Matrices " will help Engineering and Basic Science students to understand following topic of of Engineering-Mathematics:
1.how to diagonalize a 2x2 matrix
2.matrix diagonalization calculator
3.how to diagonalize a 3x3 matrix
4.diagonalization of a matrix example
5.how to know if a matrix is diagonalizable
6.diagonalization of a matrix btechguru
7.when is a matrix diagonalizable
8.Diagonalize matrix matlab
Mrs. Angel was a highly Reputed Lecturer in an MGR Janaki Arts & Science College for six months.Had One year experience as a Mathematics Teacher in The Winchester
School, Dubai.Two years experience as a Mathematics Lecturer in Skyline University,Sharjah, U. A. E.One year experience as a Mathematics Lecturer in Arignar Anna
Institute of Science and Technology.Currently working as an Assistant Professor in Hindustan University, Chennai from August 2011 till date.
We run a portal called www.btechguru.com, as part of Bodhbridge Educational Services (P) Ltd. We are India's first HD Video based training platform. We are launching a
video courses for Engineering Mathematics-I both ANNA UNIVERSITY & JNTU SYLLABUS.
Engineering Mathematics -1 Anna University Course Highlights:
1)30 sessions developed by experienced professors from various universities.
2)All the sessions are purely exam oriented.
3)40+ Recorded video sessions covering all topics from Differentialcalculus and Integral calculus and Matrices etc...
4)Basic pricing of the course is 1,200/- which comprises of doubt clearing sessions, Recorded videos, Mock tests.
Engineering Mathematics -1 JNTU Course Highlights:
1)30 sessions developed by experienced professors from various universities.
2)All the sessions are purely exam oriented.
3)40+ Recorded video sessions covering all topics from Differential calculus and Integral calculus and Matrices etc...
4)Basic pricing of the course is 1,200/- which comprises of doubt clearing sessions, Recorded videos, Mock tests.
Speak English through Hindi Language - Half of the world's population speaks in English. It is also called the language of the corporate world. Learning English is the
most sought-after thing. We are offering you a course where you can learn English through your local language and mother tongue. Learning English through Hindi will
give you an extra insight into the language and make the learning easier and more enjoyable.
To buy full course visit, https://www.btechguru.com/courses/dem...
For Engineering Courses visit, https://www.btechguru.com/courses
For GATE Courses visit, https://www.btechguru.com/GATE
For other courses visit, https://www.btechguru.com/courses/bod...
In this video you will learn how to do multiplication with 11 easily.
Visit our Official Website http://www.btechguru.com
Subscribe to our YouTube channel now and Prepare for competitive exams.
----------------------------------------¬----------------------------------------¬----
We run a portal called www.btechguru.com, as part of Bodhbridge Educational Services (P) Ltd. We are India's first HD Video based training platform has been providing
coaching since last 7 years at National level.
We have been providing online coaching through Video lecture all over India with tremendous Results since last 8 years.
We provide live classes and online classes for the subjects given below:
1. Spoken English
2. Vedic Maths
3. Reasoning (Verbal & Non-Verbal).
4. Communication Skills
6. Quantitative Aptitude.
7. Verbal Ability
8. Personality Development.
9. Interview Facing Techniques & Skills
10 .Resume Building
11. Time Management
12. IBPS
13. IIT JEE
14. Functional Grammar.
15. Placement Preparation.
16. Gate
.
- Our Experts Teaching Techniques, Shortcut Methods are unique and incomparable.
----------------------------------------¬--------------------------------
Like us on Facebook
https://www.facebook.com/btechguru.in...
----------------------------------------¬--------------------------------
Follow us on twitter
https://twitter.com/btechguru
----------------------------------------¬--------------------------------

Views: 151091
Btechguru BodhBridge ESPL

Print the matrix Diagonally. You have to print the matrix in diagonal order.

Views: 16691
Vivekanand Khyade - Algorithm Every Day

EIGEN VALUES -- EIGEN VECTORS -- MODEL MATRIX -- DIAGONAL OF THE MATRIX
Eigen Values and Eigen Vectors Introduction, Model Matrix, Diagonal of the Matrix

Views: 54806
vedupro

Matrix,
Matrices,
Matrix Multiplication,
Types of Matrices,
Diagonal Matrix,
Scalar Matrix,
Triangular Matrix,
Identity Matrix,
Adjoint Matrix,
Inverse Matrix,
Null Matrix,
Square Matrix,
Subject wise Playlists-
Electronics Devices- https://www.youtube.com/watch?v=LqyoC8xK76g&list=PL00WWA9f-4c8c8JEtwOc521ND-XGhaFkL
Analog Electronics- https://www.youtube.com/watch?v=DuJFBzcm4qw&list=PL00WWA9f-4c__I3Km5TUXrpUAsspVpbys
Control System- https://www.youtube.com/watch?v=GbDL5VAU8fk&list=PL00WWA9f-4c9yI6Nr6ot8uoOsVnJzdx1R
Signals and Systems- https://www.youtube.com/watch?v=W68Q6zRbZ6U&list=PL00WWA9f-4c8Jhs5jc3M0lW-_TF3U4GSQ
Network Analysis- https://www.youtube.com/watch?v=GBtu5lizPSY&list=PL00WWA9f-4c_10bMXg_gLkvlWLGrns4FF
Digital Electronics- https://www.youtube.com/watch?v=N82C1RXwBIM&list=PL00WWA9f-4c-Xbi57DlbC6GC82pxBkL7_
Engineering Mathematics- https://www.youtube.com/watch?v=mxb2VIuVPbw&list=PL00WWA9f-4c8SYSeEuPgpMtDir1039Na6
GATE Preparation Strategy- https://www.youtube.com/watch?v=VKbdBuzmqTE&list=PL00WWA9f-4c9X9-N321nwlRpyiUO-aOEE
Test Series- https://www.youtube.com/watch?v=kkPxBcehCZU&list=PL00WWA9f-4c_-_mtRYPNg3gesDysdECrV

Views: 1127
GATE CRACKERS

Print both the diagonals of a matrix (main diagonal and Anti-diagonal).
This video is made from the below article:
http://www.ritambhara.in/print-both-diagonals-of-a-matrix/
For detailed discussions on Interview Questions visit:
http://www.ritambhara.in/ Join our 30-days online course to prepare for coding interviews of companies like Google, Amazon, Facebook, Microsoft, etc.
Details: http://www.ritambhara.in/big-o/
Call: +91-8377803450
Email: [email protected]
Call us to conduct workshop in your college campus.
Buy our books and prepare for coding interviews on your own.
https://www.amazon.in/Kamal-Rawat/e/B...

Views: 19749
Ritambhara Tech Coding interview preparations

Hey guys! In this video I am showing you how to make a matrix in Python. If you like this video.
Plz like my video and subscribe my channel for more of such programming tutorials.

Views: 8186
TECH PHASE

Type of Matrices - Learn about Rows Matrix, Columns Matrix, Rectangular Matrix, Square Matrix, Diagonal Matrix, Scalar Matrix, Identity Matrix, Triangular Matrix, Null or Zero Matrix, Transpose matrix or Transpose of a Matrix.
1) What is Row Matrix?- 0:56
2) What is Column Matrix? - 1:30
3) What is Square Matrix? - 2:07
4) What is Rectangle Matrix?- 3:00
5) What is Diagonal Matrix? - 3:55
6) What is Scalar Matrix? - 4:51
7) What is Identity Matrix or Unit Matrix? - 5:42
8) What is Null Matrix? - 8:11
9) What is Triangular Matrix? - 9:05
- Upper Triangular Matrix - 9:18
- Lower Triangular Matrix - 10:09
10) What is Transpose Matrix or transpose of a matrix? - 11:12
Know Definition of different matrix and and also learn differences between this 10 type of matrices. The size or dimension of a matrix is defined by the number of rows and columns it contains in matrix.
Matrix in Hindi or matrices in Hindi language videos.

Views: 3929
Skill Ark

Subscribe for More Lessons: https://YouTube.com/WeSolveThem
Tip for Good Service: https://PayPal.me/WeSolveThem
Thousands of free solutions: https://WeSolveThem.com
Commenting and Full Lesson Available @ http://wp.me/p7kK3u-zd via WeSolveThem.com
Description: Linear Algebra, matrix multiplication, LDU decomposition, LDU factorization, LU factorization, LU decomposition, Identity matrix, REF(A), RREF(A), Row reduction, row elimination. Upper diagonal, Lower diagonal Diagonal. Using a calculator to solve matrices. Gauss elimination Elementary matrix
Half off 12 months -- use code HALFOFFNOW @ http://wesolvethem.com/register
Copyright © 2013 → ∞ WeSolveThem.com - JJtheTutor, Inc. All rights reserved | Made By Students, For Students.

Views: 4844
JJtheTutor

Multiply Matrix using calculator , If you want to Multiply two matrix then by using calculator you can easily calculate.
using calculator for solving your time will be saved and correct result.
after watching the video you will able to Multiply matrix easily using calculator.using 991es plus calculator Matrix multiplication is done.Multiply Matrix in calculator.Multiplication up to 3x3 matrix can be done in calculator.Multiply Matrix A and B in calculator.

Views: 373075
Arohan kumar

http://www.indiastudychannel.com/r/sujoy70.aspx
In this video I'll tell you how to find Sum & Product of Eigen Values of a 3x3 matrix very easily.
I've uploaded videos on Statistics,Numerical Methods,
Business & Financial Mathematics,Operation Research,Computer Science & Engineering(CSE),Android Application Reviews,India Travel & Tourism,Street Foods,Life Tips and many other topics.
And a series of videos showing how to use your scientific calculators Casio fx-991ES & fx-82MS to do maths easily.
Click my YouTube channel's link below to watch them.
Subscribe to my youtube channel below-
YouTube- http://www.youtube.com/sujoyn70
Blog- http://www.sujoyn70.blogspot.com

Views: 9754
Sujoy Krishna Das

multiplication by a diagonal matrix, a linear system written as matrix product, substitution as matrix multiplication, matrix multiplication as a sum of products of columns with rows.

Views: 103
Omnia A

In this video explaining one problem of reduce to diagonal matrix. This method is very good and easy to understand.Any one can solve this method.
-~-~~-~~~-~~-~-
Please watch: "Laplace transform of unit step function fourth problem(PART-4) by easy maths easy tricks"
https://www.youtube.com/watch?v=_7ICtZQYYFw
-~-~~-~~~-~~-~-

Views: 27237
EASY MATHS EASY TRICKS

FACTS ABOUT MATRIX MULTIPLICATION
http://www.starsoutline.com/
Triangular matrix, Diagonal matrix, Scalar matrix, Identity matrix, Symmetric matrix, Skew-symmetric matrix, Direct Sum, Transpose of a matrix, Multiplication of Matrix,
Matrix, Best Matrix Video, Best Matrix Video, maths tricks, class xii maths,class 12th maths, Operations of Matrices, rank of matrix, ncert solutions for class 12 maths

Views: 127
Stars Outline

When a matrix is block diagonal or block triangular, then its eigenvalues are the eigenvalues of the two blocks, but the eigenvectors may be harder to come by.

Views: 10698
Lorenzo Sadun

Math Tutor Series for Matlab Programming.

Views: 12915
Ahmed Hamdy

This video explains how to write a matrix as a product of elementary matrices.
Site: mathispower4u.com
Blog: mathispower4u.wordpress.com

Views: 106870
Mathispower4u

Matrix Multiplication
---------------------------------------------
Matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring. The matrix product is designed for representing the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, physics, and engineering.[1][2] In more detail, if A is an n × m matrix and B is an m × p matrix, their matrix product AB is an n × p matrix, in which the m entries across a row of A are multiplied with the m entries down a column of B and summed to produce an entry of AB. When two linear maps are represented by matrices, then the matrix product represents the composition of the two maps.
The definition of matrix product requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications, the matrix elements belong to a field, although the tropical semiring is also a common choice for graph shortest path problems.[3] Even in the case of matrices over fields, the product is not commutative in general, although it is associative and is distributive over matrix addition. The identity matrices (which are the square matrices whose entries are zero outside of the main diagonal and 1 on the main diagonal) are identity elements of the matrix product. It follows that the n × n matrices over a ring form a ring, which is noncommutative except if n = 1 and the ground ring is commutative.
A square matrix may have a multiplicative inverse, called an inverse matrix. In the common case where the entries belong to a commutative ring r, a matrix has an inverse if and only if its determinant has a multiplicative inverse in r. The determinant of a product of square matrices is the product of the determinants of the factors. The n × n matrices that have an inverse form a group under matrix multiplication, the subgroups of which are called matrix groups. Many classical groups (including all finite groups) are isomorphic to matrix groups; this is the starting point of the theory of group representations.
--------------------------------------------------------------------------
In this video we show you how to multiply matrices in an easy way. Although we are doing the same thing but the process looks easy.
If you liked this video
Then HIT the like button.
SHARE this video as much as you can
And don't forget to subscribe to our channel.
As we come up with more videos like this.
~~~~~~~~~~THANK YOU~~~~~~~~

Views: 320
Magnus Academy

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 4171
MathTheBeautiful

Topics: Types of Matrices, Column matrix, Row matrix, Square matrix, Diagonal matrix, diagonal elements, Scalar matrix, Identity matrix, Zero matrix, Equal matrices, Some solved examples or questions related to the concept.
Feel free to comment for any issue or doubt. And if you LIKE the video then don't forget to SUBSCRIBE the channel, SHARE it with your friends and also give a THUMBS UP. Thank You!
Connect to us on Facebook @ https://www.facebook.com/excelclassespatna/

Views: 6426
Excel Classes

C Program to find the sum of all diagonal elements of a given matrix.
Loop variable i - represents rows
Loop variable j - represents columns
diagonal elements are those where indexes i==j

Views: 13547
Sundeep Saradhi Kanthety

Prove that the Set of 2 x 2 Diagonal Matrices with Nonzero Entries Forms a Group
In this video we prove the set of 2 x 2 diagonal matrices with nonzero entries forms a group under regular matrix multiplication.

Views: 63
The Math Sorcerer

In this video explaining VTU first semester module 5 one very useful problem.Given matrix is reduce to the diagonally and very interesting problem.
-~-~~-~~~-~~-~-
Please watch: "Laplace transform of unit step function fourth problem(PART-4) by easy maths easy tricks"
https://www.youtube.com/watch?v=_7ICtZQYYFw
-~-~~-~~~-~~-~-

Views: 1965
EASY MATHS EASY TRICKS

Tiagabine generic lipitor

Isopto carpine generic viagra

Diltiazem er 180 mg capsules side effects

No side effects from zoloft 100mg

© 2019 Rides of magic kingdom

Philosophys powerful influence on the formation and development of the cultures of the West should not obscure the influence it has also had upon the ways of understanding existence found in the East. Every people has its own native and seminal wisdom which, as a true cultural treasure, tends to find voice and develop in forms which are genuinely philosophical. One example of this is the basic form of philosophical knowledge which is evident to this day in the postulates which inspire national and international legal systems in regulating the life of society. Nonetheless, it is true that a single term conceals a variety of meanings. Hence the need for a preliminary clarification. Driven by the desire to discover the ultimate truth of existence, human beings seek to acquire those universal elements of knowledge which enable them to understand themselves better and to advance in their own self-realization. These fundamental elements of knowledge spring from the wonder awakened in them by the contemplation of creation: human beings are astonished to discover themselves as part of the world, in a relationship with others like them, all sharing a common destiny. Here begins, then, the journey which will lead them to discover ever new frontiers of knowledge. Without wonder, men and women would lapse into deadening routine and little by little would become incapable of a life which is genuinely personal.