- #1
eckiller
- 44
- 0
This is a follow up to a post I made a couple days ago.
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.
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.