This is a follow up to a post I made a couple days ago.(adsbygoogle = window.adsbygoogle || []).push({});

Basically, I needed to find a set of a-orthogonal vectors given that A is positive definite.

Is the following satisfactory?

Pick the standard basis B = {e1, ..., en}.

Then consider ei' A ej such that i != j.

Since A is positive definite, A can be factored as A = L'L.

Then (ei' L')(L ej)

However, for all ei and ej s.t. i != j,

(ei' L')(L ej) = 0

ei' A ej = 0

<ei, Aej> = 0

So I have determined an A-orthogonal set.

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# A-orthogonal vector set

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