Nilpotent Matrix. Nilpotent Matrix is a square matrix such that the product of the matrix with itself is equal to a null matrix. A square matrix M of order n × n is termed as a nilpotent matrix if M k = 0. Here k is the exponent of the nilpotent matrix and is lesser than or equal to the order of the matrix( k < n). The order of a nilpotent matrix is n × n, and it easily satisfies the ...

2025年1月21日 · A square matrix M is called nilpotent if there exists a positive integer k such that:. M k = 0. where 0 represents the zero matrix of the same dimensions as M. The smallest such integer k is called the index or degree of the nilpotent matrix.. A nilpotent matrix is a square matrix that has an equal number of rows and columns and also it satisfies matrix multiplication.