Orthogonal Matrix and its properties | Idempotent Matrix | Nilpotent Matrix | Involutory Matrix

#OrthogonalMatrix #IdempotentMatrix #NilpotentMatrix #InvolutoryMatrix #matrix #ruchinbansal #ruchinbansalmaths #iitjee

In this video we going to explain about "Orthogonal Matrix ,Idempotent Matrix, Nilpotent Matrix, Involutory Matrix".

This Lecture Covered:
How to find Orthogonal matrix ?
What are Idempotent matrix ?
What are Nilpotent matrix ?
How can we Involutory Matrices?

1. Orthogonal matrices are square matrices which when multiplied with its transpose matrix results in an identity matrix. So, for an orthogonal matrix, Ax(Transpose of A) = I
To test whether a matrix is an orthogonal matrix, we multiply the matrix to its transpose. If the result is an identity matrix, then the input matrix is an orthogonal matrix.
A square matrix with real numbers is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

2. An involutory matrix is a matrix that is its own inverse. That is, multiplication by matrix A is an involution if and only if AxA = I. Involutory matrices are all square roots of the identity matrix.

3. An idempotent matrix is a matrix which, when multiplied by itself, yields itself. For this product to be defined, must necessarily be a square matrix.

4. A square matrix A is called nilpotent if there is a non-negative integer k such that A^k is the zero matrix. The smallest such an integer k is called degree or index of A.

In this session learn the complete details about “What are Idempotent matrix, nilpotent, orthogonal,Involutory” which is the most important part of MATRICES for all boards and competitions.
Complete guidance about Matrices MATHS CBSE and Other Boards exams.

Ruchin Bansal Sir enlightens you with the “Idempotent matrix, nilpotent, orthogonal,Involutory" and giving tips on how to solve and react with the problems easily with in-depth explanations.

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