1,573 views
3 votes
3 votes

A) what are the eigen values of Orthogonal matrix ? Describe general properties.

B) what are the Eigen value of skew-symmetric matrix ? Describe general properties.

C) Are there any speciality in Eigen values of Symmetric, Hermitian, Skew- Hermitian, Unitary . If there , describe them also.

1 Answer

0 votes
0 votes

[A]

Any real eigenvalue of an orthogonal matrix has absolute value 1. Actually, it is also true that each complex eigenvalue must have modulus(magnitude) 1

[B][C]

Eigen values of real symmetric and hermitian matrices are real

Eigen values of real skew symmetric and skew hermitian matrices are either pure imaginary or zero

Eigen values of unitary matrix have magnitude 1

Source:

https://www.quora.com/Can-you-define-unitary-matrix-and-show-that-the-eigen-values-of-unitary-matrix-are-of-unit-modulus

http://quiz.geeksforgeeks.org/eigen-values-and-eigen-vectors/

Related questions

1 votes
1 votes
0 answers
1
1 votes
1 votes
0 answers
3
Shamim Ahmed asked Jan 4, 2019
506 views
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?