Please help me I know that all elements of $-A^2$ is positive-semidefinite, but I don't know the next.
2026-03-29 04:44:05.1774759445
Suppose that $A$ is an $m\times m$ skew-symmetric matrix. Show that $-A^2$ is a nonnegative definite matrix.
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$$A = -A^T \implies -x^TA^2x = -x^T(-A^T)Ax = (Ax)^T(Ax) = \left\|Ax\right\|^2$$