This isn't really homework, but close enough. I suppose this is quite simple, but my head's all tangled up for today. Anyways, Given the real symmetric matrix LTL = UDUT, find L. I suppose L = +- D1/2UT, and it's clear this choice of L satisfies the given equation. But can it be proven that the above L actually follows from the given equation? i.e. LTL = UDUT = (D1/2UT)T(D1/2UT) <=> L = +- D1/2UT? Am I making any sense?