Symmetric and Skew Symmetric Matrices:

A square matrix A = [aij] is said to be symmetric when aij = aji for all i and j, i.e. A = A¢. If aij = -aji for all i and j and all the leading diagonal elements are zero, then the matrix is called a skew symmetric matrix, i.e. A = – A’.


Orthogonal Matrix:

Any square matrix A of order n is said to be orthogonal if AA¢ = A¢ A = .

Idempotent Matrix:

A square matrix A is called idempotent provided it satisfies the relation A2 = A.

Involuntary Matrix:

A square matrix A is said to be involuntary if A2 = I.

Nilpotent Matrix:

A square matrix A is called a nilpotent matrix if there exists a positive integer m such that
Am = O, where O is a null matrix. If m is the least positive integer such that Am = O, then m is called the index of the nilpotent matrix A.

« Click Here for Previous Topic Click Here for Next Topic »

CBSE Class 12 Maths Matrices All Topic Notes  CBSE Class 12 Maths All Chapters Notes

You wish to report grammatical or factual errors within our online articles, you can let us know using the article feedback form.