A nilpotent matrix (P) is a square matrix, if there exists a positive integer ‘m’ such that Pm = O. In other words, matrix P is called nilpotent of index m or class m if Pm = O and Pm-1 ≠ O. Here O is the null matrix (or zero matrix). Nilpotent matrix Examples The examples of … Read more
An involutory matrix is a square matrix which when multiplied by itself, gives the resultant matrix as identity matrix. In other words, matrix B is called involutory if B2 = I. Here I is the identity matrix having size same as of matrix B. Involutory matrix Examples The examples of 2 x 2 involutory matrices are 1. \[\begin{bmatrix} 4 … Read more
An idempotent matrix is a square matrix which when multiplied by itself, gives the resultant matrix as itself. In other words, a matrix P is called idempotent if P2 = P. Idempotent matrix Examples The examples of 2 x 2 idempotent matrices are 1. \[\begin{bmatrix} 0 &0 \\ 0& 0 \end{bmatrix}\] 2. \[\begin{bmatrix} 1 &0 … Read more
A diagonal matrix is a type of square matrix in which all off-diagonal elements are zero. It is noted that the diagonal elements may or may not be zero. In this article, you will learn all the important properties and conditions. Condition for diagonal matrix Suppose P be a square matrix having ‘i’ rows and … Read more
A scalar matrix is a special case of a diagonal matrix, in which all diagonal elements are equal and all off-diagonal elements are zero. A scalar matrix is always a square matrix and hence the size of this matrix will be n x n. Condition for Scalar Matrix Let M is a square matrix having … Read more