The density of the inverse and pseudo-inverse of a random matrix

✍ Scribed by Ingram Olkin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 184 KB
• Volume: 38
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(97)00163-6

✦ Synopsis

Given an absolutely continuous density of a random matrix X, we study the density of the inverse when X is a p x p symmetric, triangular and arbitrary matrix, and the pseudo-inverse when X is rectangular. In the latter case we provide alternative proofs to that of Zhang (1985), who first obtained this density. @ 1998 Elsevier Science B.V. All rights reserved Suppose that X is a p x n (p<,n) random matrix with a density that is a function of XX', say f(XX').

Then the density of S =XX / is ~P----~" ISlC"-p-~v= f(s), (l) Fp(n/2