Linear Algebra
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
A.1 Properties of Matrices
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
• det(AB) = det(A)det(B), where det(⋅) denotes the determinant of a square matrix. As ...
Get Machine Learning now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.