Essays on the theory and applications of linear algebra by the renowned author of Introduction to Linear Algebra.

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.