Description
Book SynopsisLinear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems.
Trade ReviewLinear Algebra and Matrices: Topics for a Second Course by Helene Shapiro succeeds brilliantly at its slated purpose which is hinted at by its title. It provides some innovative new ideas of what to cover in the second linear algebra course that is offered at many universities...[this book] would be my personal choice for a textbook when I next teach the second course for linear algebra at my university. I highly recommend this book, not only for use as a textbook, but also as a source of new ideas for what should be in the syllabus of the second course." - Rajesh Pereira,
IMAGETable of Contents
- Preliminaries
- Inner product spaces and orthogonality
- Eigenvalues, eigenvectors, diagonalization, and triangularization
- The Jordan and Weyr canonical forms
- Unitary similarity and normal matrices
- Hermitian matrices
- Vector and matrix norms
- Some matrix factorizations
- Field of values
- Simultaneous triangularization
- Circulant and block cycle matrices
- Matrices of zeros and ones
- Block designs
- Hadamard matrices
- Graphs
- Directed graphs
- Nonnegative matrices
- Error correcting codes
- Linear dynamical systems
- Bibliography
- Index
