Essays in Linear Algebra

The renowned mathematician and educator Gilbert Strang presents a collection of expository papers on the theory and applications of linear algebra, accompanied by video lectures on http: //ocw.mit.edu. The essays are diverse in scope and range from purely theoretical studies on deep fundamental principles of matrix algebra to discussions on the teaching of calculus and an examination of the mathematical foundations of aspects of computational engineering. One thing these essays have in common is the way that they express both the importance and the beauty of the subject, as well as the author's passion for mathematics. This text will be of practical use to students and researchers across a whole spectrum of numerate disciplines. Furthermore, this collection provides a unique perspective on mathematics and the communication thereof as a human endeavour, complemented as these essays are by commentary from the author regarding their provenance and the reaction to them

Gilbert Strang, Massachusetts Institute of Technology
Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs. In addition, he is the author of many textbooks and his service to the mathematics community is extensive, having spent time as President of SIAM, Chair of the Joint Policy Board for Mathematics as well as membership of various other committees and boards. The awards that Professor Strang has received for his research and teaching include the Chauvenet Prize (1976), the Award for Distinguished Service (SIAM, 2003), the Graduate School Teaching Award (MIT, 2003) and the Von Neumann Prize Medal of the U.S. Association for Computational Mechanics (2005), among others. He is a Member of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences and an Honorary Fellow of Balliol College, Oxford.

Part I. Essays in Linear Algebra:
1. Perfect bases for the four subspaces
2. Four subspaces from a graph
3. My favourite matrix
4. The ultimate in echelon forms
5. Diagonalizing a symmetric matrix
6. Pascal's triangle in three matrices
7. Can the factors be sparse?
8. The eigenvalues of AB + BA
9. Factoring into very special matrices
10. Toeplitz matrices and circulants
11. The joint spectral radius of A and B
12. Banded matrices have remarkable inverses
Part II. Essays in Calculus:
13. The fundamental theorem of calculus
14. The great function of calculus
15. Thin strips and small triangles in calculus
16. Chaos in Newton's method
17. Optical illusions for y = sin n
Part III. Essays in Applied Mathematics:
18. The principles of applied mathematics
19. A minimum equals a maximum
20. Aiming directly at the solution
21. A chair through a door
Part IV. Essays in Computational Science:
22. Eight cosine transforms
23. The ideas behind finite elements
24. The Strang–Fix conditions
25. Wavelets in music and television
26. Scaling functions lead to wavelets
27. Old and new splitting methods
An essay about books
List of publications
Index.