April 2015
Intermediate to advanced
1062 pages
40h 35m
English
Chapter Outline
A.1 Properties of Matrices 1013
Matrix inversion lemmas 1014
Matrix derivatives 1014
A.2 Positive Definite and Symmetric Matrices 1015
A.3 Wirtinger Calculus 1016
References 1017
Let A,B,C, and D be matrices of appropriate sizes. Invertibility is always assumed, whenever a matrix inversion is performed. The following properties hold true.
• (AB)T = BTAT.
• (AB)−1 = B−1A−1.
• (AT)−1 = (AT)−1.
• trace{AB} = trace{BA}.
• From the previous, we readily get
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• det(AB) = det(A)det(B), where det(⋅) denotes the determinant of a square matrix. As ...