Essays in Linear Algebra（高清带书签文字版）Essays In Linear

文件名称: Essays in Linear Algebra（高清带书签文字版）

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详细说明：Essays In Linear Algebra，吉尔伯特的线性代数论文集，高清带书签文字版，仅此一家。附件是英文版的。Essays in Linear Algebra Co by C ISBN978-0-9802327-6-9 All rights rescrved. No part of this work may bc reproduced or stored or transmited means, including photocopying, without written permission from ley -Cambridge Press. Translation in any language is strictly prohibited. Typeset by Valutone(www, valuitonc co. in) Printed in the United Statcs of America 98765432 QA184792012 Introduction to Linear Algebra, 4th Edition (2009)Gilbert Strang 978-0.9802327-1-4 Wavelets and Filter Banks, Gilbert Strang Truong Nguyen 978-0-9614088-7-9 Introduction to Applied Mathematics, Gilbert Strang 978-0-9614088-c-0 Calculus, Gilbert Strang, Second edition(201D)978-0-9802327-4-5 Algorithms for Global Positioning, Kai Borre Gilbert Strang (2012)978-0-9802327-3-8 An Analysis of the Finite Element Method, Gilbert Strang George Fix (2008) Wellesley- Cambridge Press gsmath. mit. edu Box math. mit. edu/gs Wellesley MA 02482USA phone t781)431-8488 Our books are also distributed by SIAM (n North America Linear A This provides video lectures of the full li Course material is on the teaching website: web mit. edu/18. 06 Highlights of Calculus(17l The cover design was the inspiration of two creative artists/designers Lois Sellers(birchdesignassociates com) and Gail Corbett "Walking Man "by Alberto Giacometti(1960) O 1 Succession Giacometti and Artists Rights S s) New York/ADAGP, P O Albright-Knox Art Gallery, Buffalo NY/ Art Resource, NY(image) This six-foot sculpture is the most highly valued art work ever sold at auction. Preface nds one part of a life. Writing has been an extremely happy part, bject has often been linear algebra. The words and the ideas are mathemalical nderncaLh those words I hope you will feel an urgent message We can understand this subject and teach it better It is truc that mathematics is not usually assaciated with urger orally calm and deliberate (and they should be). My point is that thousands o professionals are using mathematics, and millions of students are learning it. This is an intense human effort and it needs to be productive ink of two separate pleasures in writing. The first is for one person only. Sittin At other times you deas are right and 二二 ork is not rea to feel that the but there is the second pleasure comes much later and more slowly. The reader replies! In ay you have connected (the Internet makes this possible). It is not Facebook natch.com,butitisverysatisfyingwhenreadersrespondThereisabigdifference between depositing research papers into an archive and a two-way communication This book mostly contains expository papers. They are scattered in many journals and it seemed sensible to bring them together. And also(this is the new part of the book)there as something to say about each one-how the paper happened to be written, the responses that came after publication, and very often a fresh look at the mathematical ideas. I enjoyed writing those cssays. You will find open problems y been the most widely read. Every matrix produces four fundamental subspaces (the nullspace ancl the n spaces of A and A ). Those subspaces have infinitely bases. A perfect choice f the bases will diagonalize the matrix and display its most basic properties-its rank, its norm, and its inverse (or pseudoinverse). At the start we only know the entries in the matrix Preface obtuse when rescaled. And here is the amazing fundamental fact. when the six coordi nates of the corners have a normal distribution, the points (representing triangles)are uniformly distributed on the surface of the sphere. Now we only have to see which part of this triangle space contains acute triangles. Looking down from far above the hemisphere, we see the circle in the following figu Each dot represents a random triangle. Right triangles with u2+b2=(2 lie on a white line (remember that the coordinates of triangle space are now a2b2, c2).The other right triangles with a2+(2=b2 and b2+c2=u give the other white lines side those white lines(which are semicircles on the sphere )are all the acute triangl pcs, where (a, b.c) is dray Right triangles fall on the white equilateral triangle and all the acute triangles are inside When you cut down along the white lines, cTion of the The Grow des, and exercise in calculus. (It is only easy when you h have plenty of practice nize that we are getting the sane answer 4 from Iwo ctures of triangle space. We dont know why Let me compare and contrast the two pictures, a big triangle based on angle hemisphere based on side lengths squared, The outer boundaries in both case tally fiat triangles(onc angle is zero). The right triangles in both pictures lie on hes,with equations like A+B=90 for angles and (2+b2=2 for side Then the other angle is C= 90 and the other side has c=2 by Pythagoras. The points ( the triangles) are uniformly distributed on the plane A+ B+C=180 and the sphere ditte lat raction for the acute triangles, or is this an accident The hemisphere is truly the better picture (and it was known to David Kendally point on the hemisphere. That will be in our paper and on our websites, before thi book of essays is pu The beauty of mathematics is not superficial. It needs an effort to be appreciated. Like art and music and literature, the depth varies. Few of us could follow the proof of Ferma last theorem, that a+b"=c is impossible for integers a, b, c and n>2. But the stor of that proof--and perhaps someday of the Riemann hypothesisis an inspiration. All of rtunately, lincar algebra is not so difficult. You will see the "Big Picture"of a matrix on page I, and its meaning steadily energes as you see examples. It is such a wonderful chance, that this part of mathematics has become so important. Those acute triangles were mostly entertainment, but Ar= h and Ax dx are constantly needed and used I hope that some of these essays will please you. If you see some corner of mathematics a new way. then they have succeeded. They were a pleasure to write WEBSITES FOR COURSES AND BOOKS math. mit. edu/gs (Home page) web. mit. edu/18.06 math. mit. edu/1808 math. mit. ed br math.mit.edu/cse (Computational Science and Engineering) t. edu/calcul ocw.mit. edu (MIT Open Course Ware Table of Contents A Essays in Linear Algebra I Perfect Bases for the Four Subspace enta! Theorem of Linear Aigebra 2 Four Si om a Graph Graphis, Matrices, and Subspaces 3 My Favorite Matrix Echelon Form Ron Reduction of a Matrix and A= CaB Proofs of the Spectral Theorem 7 Can the Factors be Sparse? Marices 8 The e eigenvalues of AB+B Eigenvalues of Joron Producrs Into very Special Matrices 10 Toeplitz Matrices and Circulants A Proposal for Toeplitz Matrix Calculations 11 The Joint Spectral Radius of A and B 12 Banded Matrices Have Remarkable Inverses 13 The Fundamental Theorem of caleulu Sums and Diferences vs, Integrets and Derivatives 14 The Great function of calculus Introducing e- IX 15 Thin Strips and Small Triangles in Calculus Pular Area is the Averge of Strip Areas 17 Optical Illusions for y= sin it s238201 C Essays in Applied Mathematics Duality in ihe Clevsnoni 21 A Chair Through a Door The width of a Chiai D Essays in Computational Science 23 The Ideas bebind Piecewise polynomials and the finite element method 4 The Strang-Fix Conditions The Finite Element Method avid Approximation Theory 25 Wavelets in Music and Television 26 Scaling f 27 Old and tting Methods id Comprison of Diference Schemes E An Essay About Books F List of Publications G Index rt A Essays in Linear Algebra

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