Random Matrix

Definition

$\mathbf{Z}=[Z_{ij}]$ where each $Z_{ij}$ is a Random Variable

A matrix whose components are random variables.

Operations

Expectation

Let $\mathbf{Z}$ be an $m\times n$ matrix. $E(\mathbf{Z})=[E(Z_{ij})]$

Linear Combination

Let $\mathbf{Z}$ be an $m\times n$ matrix. $E(A\mathbf{Z}B+C)=AE(Z)B+C$ where $A,B,C$ are $l\times m$, $n\times p$, and $l\times p$ matrices, respectively, of constants.