Eigen Values of special matrices

Question

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.

Comments

I have read -

a) Eigen values of Orthogonal matrix have magnitude 1.

b) possible Eigen values of skew- symmetric matrix are '0' or imaginary.

     please verify.

Answer 1

[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/