Essays in linear algebra (Q2884705)

The volume under review brings together 27 classic articles on linear algebra and some of its relevant applications to computational science, applied mathematics, and calculus, each introduced by a new essay. Some of the central themes of this book are: the four fundamental subspaces and perfect bases; an effective way to introduce the exponential function; the finite element method and its accuracy; wavelets and signal processing; the fundamental theorem of calculus; the joint spectral radius; and a great variety of matrices (Toeplitz, circulant, banded, incidence, graph Laplacian, and Pascal matrices).NEWLINENEWLINEThe present volume contains the following parts. 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.NEWLINENEWLINEAll essays present historical background, the current state, and unsolved problems.NEWLINENEWLINEIn summary, this delightful book is a most welcome addition to the library of any mathematician with an interest in applied linear analysis.