Appendix D: Essentials of Linear Algebra
Joseph L. Hellerstein, Yixin Diao, Sujay S. Parekh, Dawn M. Tilbury · 2004
Essentials of Linear AlgebraIn this appendix we provide a brief review of results from linear algebra that are needed for state-space analysis.We state some definitions related to matrices and some properties of matrices without proof.For a deeper understanding, the reader is encouraged to refer to a linear algebra text (e.g., [37]). D.1 MATRIX INVERSE, SINGULARITYAn n × n matrix A is an invertible matrix if there exists another n × n matrix P such that AP = PA = I.If the inverse exists, it is unique and is typically denoted as A -1 .Further, it is easy to see that (A -1 ) -1 = A.If A does not have an inverse, it is called singular.