- #1

N00813

- 32

- 0

## Homework Statement

If M is a real anti-symmetric n x n matrix, M^2 is a real symmetric matrix. Show that M^2 is a non-positive matrix, i.e. x(transposed) M^2 x <= 0, for all vectors x.

## Homework Equations

det(M) = (-1)^n det (M)

## The Attempt at a Solution

I attempted to use the relevant equation above to find the determinant of M^2, and found that it is >=0. Diagonalising M^2 gives me the matrix of diagonal eigenvalues, which shares the same determinant as M^2. Thus, in the eigenvalue basis, I proved y(trans) D y >=0, which is the opposite of what the question wants.