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CBSE Class 12 Maths Notes: Matrices – Special Matrices

by Anand Meena
April 22, 2019
in 12th Class, Class Notes
Reading Time: 2min read
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SPECIAL MATRICES

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.

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Tags: CBSE NotesClass 12 NotesClass 12thFree Notes

Anand Meena

Full time entrepreneur, likes to indulge in writing reviews about the latest technologies apart from helping students in career and exam related topics.

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