Square, Diagonal, Unit, Triangular Matrices
Square Matrix
A matrix in which a number of rows are equal to the number of columns is called a square matrix. That is, a matrix of order is often referred to as a square matrix of order .
Diagonal Matrix
In a square matrix of order , the elements are called the principal diagonal or simply the diagonal or main diagonal or leading diagonal elements.
A square matrix is called a diagonal matrix if whenever
Unit matrix
A square matrix in which all the diagonal entries are 1 and the rest are all zero is called a unit matrix. Thus, a square matrix is said to be a unit matrix if if , and if .
Upper triangular matrix
A square matrix is said to be an upper triangular matrix if all the elements below the main diagonal are zero.
Lower triangular matrix
A square matrix is said to be a lower triangular matrix if all the elements above the main diagonal are zero.
Triangular matrix
A square matrix which is either upper triangular or lower triangular is called a triangular matrix.