Chapter 16
Matrix Equalities and Inequalities
Michael Tsatsomeros
Washington State University
In this chapter, we have collected classical equalities and inequalities regarding the eigenvalues, the singular values, the determinant, and the dimensions of the fundamental subspaces of a matrix. Also included is a section on identities for matrix inverses. The majority of these results can be found in comprehensive books on linear algebra and matrix theory, although some are of specialized nature. The reader is encouraged to consult, e.g., [HJ85], [HJ91], [MM92], or [Mey00] for details, proofs, and further bibliography.
Recall that σ(A) denotes the (multiset) of the eigenvalues of a square matrix A.
16.1 Eigenvalue Equalities and Inequalities
The ...
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