Handbook of Linear Algebra, 2nd Edition

Chapter 56

Unsymmetric Matrix Eigenvalue Techniques

David S. Watkins

Washington State University

The definitions and basic properties of eigenvalues and eigenvectors are given in Section 4.4. A natural generalization is presented here in Section 56.1. Algorithms for computation of eigenvalues, eigenvectors, and their generalizations will be discussed in Sections 56.2 and 56.3.

If a large fraction of a matrix’s entries are zeros, the matrix is called sparse. A matrix that is not sparse is called dense. Dense matrix techniques are methods that store the matrix in the conventional way, as an array, and operate on the array elements. Any matrix that is not too big to fit into a computer’s main memory can be handled by dense matrix techniques, regardless ...