Question

Let A be a 4x4 real skew-symmetric matrix. Then the possible eigenvalues of A are,

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Answer 1

The possible set of eigenvalues of a 4×4 skew symmetric, orthogonal matrix. As it is real skew symmetric so eigenvalues may be 0 or Purely Imaginary, and as it is orthogonal so determinant must be 1 or −1. So 1 may be the possible set.

Answer:

The possible set of eigenvalues of a 4×4 Real skew symmetric, orthogonal matrix is

1.{±i}

2.{±i,±1}

3.{±1}

4.{±i,0}