I'm having a bit of a brain fart here. Given a positive definite quadratic form(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum \alpha_{i,j} x_i x_j [/tex]

is it possible to re-write this as

[tex] \sum k_i x_i^2 + \left( \sum \beta_i x_i \right)^2[/tex]

with all the k_{i}positive? I feel like the answer should be obvious

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# Simplifying quadratic forms

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