Question

3+
* show that the mation A=
is skew heimition.
(-2+1​

Answer 1

Answer:I present a slight modification on the answer to a very similar question. I assume we are working over the complex numbers.

Recall the eigenvalues of a skew-Hermitian matrix are imaginary. So the set of eigenvalues of J=I−A cannot contain zero, and the matrix is invertible. We then have W=J−1JH. it remains to compute:

J−1JH(J−1JH)H=J−1JHJ(J−1)H=J−1JHJ(JH)−1

Note now that J and JH commute.

J−1JHJ(JH)−1=J−1JJH(JH)−1=I.

The other computation is almost exactly the same.

Step-by-step explanation: