Review of Matrix Algebra

Diagonal matrix

A diagonal matrix is a matrix (usually a square matrix) in which the entries outside the main diagonal (↘) are all zero. The diagonal entries themselves may or may not be zero.

Square matrix

A square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n.

Upper or Lower triangular matrix

A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero.

Symmetric matrix

A symmetric matrix is a square matrix that is equal to its transpose.

Partitioned matrix

In mathematics, a block matrix or a partitioned matrix is a matrix which is interpreted as having been broken into sections called blocks or submatrices.[1] Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines which break it out, or partition it, into a collection of smaller matrices.[2] Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.

Vector

a matrix with one column

Matrix

a rectangular, two dimensional array of elements, generally denoted by a single uppercase Roman letter in boldface

Zero matrix

a zero matrix or null matrix is a matrix with all its entries being zero

deimension Arxc

r = rows, c = columns

Scalar

single number, vector, matrix

Identity matrix

the identity matrix or unit matrix of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

A={aij}

the matrix whose ith jth element is aij