- #1

holezch

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## Homework Statement

Prove that T is positive definite if and only if

[tex]\sum_{i,j} A_{ij}a_{j}\bar{a_{i}} > 0 [/tex]

for any non-zero tuple (a1, .................... , an )

Let A be [tex][ T ]_{\beta} [/tex]

where [tex] \beta [/tex] is an orthogonal basis for T

## The Attempt at a Solution

the sum looked like the matrix multiplication of a n-tuple and a matrix A, so I looked into that and couldn't get anything.. any hints please? I'm also struggle to realize what significant that sum could have, right now it doesn't even mean anything to me.

Thanks!