Appendix A: Review of Matrix Algebra
2012
We present here a brief review of some concepts that are assumed as background for the text.Good references include Gantmacher (1977), Brogan (1974), and Strang (1980). A.1 BASIC DEFINITIONS AND FACTSThe determinant of an n × n matrix is symbolized as |A|.If A and B are both square, then |A| = |A T |, (A.1-1) |AB| = |A| • |B|, (A.1-2) where the superscript T represents transpose.If A ∈ C m×n and B ∈ C n×m (where n can equal m), then trace(AB) = trace(BA) (A.1-3) |I m + AB| = |I n + BA|.(A.1-4) (C represents the complex numbers.)For any matrices A and B , (AB) T = B T A T (A.1-5) and if A and B are nonsingular, then