What is an Idempotent Matrix

Idempotent Matrix

A matrix is defined as a rectangular array of numbers that are arranged in rows and columns. The size of a matrix can be determined by the number of rows and columns in it. A matrix is said to be an “m by n” matrix when it has “m” rows and “n” columns and is written as an “m × n” matrix. For example, a matrix of order “5 × 6” has five rows and six columns. We have different types of matrices like rectangular matrices, square matrices, null matrices, triangular matrices, symmetric matrices, etc.

Idempotent Matrix Definition

An idempotent matrix is defined as a square matrix that remains unchanged when multiplied by itself. Consider a square matrix “P” of any order, and the matrix P is said to be an idempotent matrix if and only if P2 = P. Idempotent matrices are singular and can have non-zero entries. Every identity matrix is also an idempotent matrix, as the identity matrix gives the same matrix when multiplied by itself.