1.1 Matrix

We define a matrix \begin {equation} \tag {1} A = (a_{ij}) = \begin {pmatrix} a_{11} & a_{12} & \cdots & a_{1p}\\ & a_{22} & \cdots & a_{2p}\\ \vdots & \vdots & & \vdots \\ \vdots & \vdots & & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{np}\\ \end {pmatrix} \end {equation} as an \(n\times p\) matrix of either constants or random variables.

Its transpose is denoted by \[A' = A^T = (a_{ij})_{ji}\qquad i = 1,2,\ldots ,n\qquad j=1,2,\ldots ,p\]

Note 1.1.