# Why do we use quadratic form for random vectors? [closed]

I am studying linear regression. I have studied this in the past, but this is my first time exposing myself to the matrix form of multiple linear regression. My matrix algebra/linear algebra skills are a little rusty and I have been trying to review/relearn a lot of the material so I can better understand the multiple linear regression proofs.

One thing that keeps coming up is quadratic form of random vectors. I am working through some regression proofs using the quadratic form, but I am not sure I fully understand its purpose?

If anyone can explain why they are used, or their purpose either generally or with respect to regression I would be extremely thankful!

## closed as unclear what you're asking by Xi'an, Yves, user158565, Taylor, BenMar 8 at 0:14

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• Succinct notations make mathematical statements much easier to read and understand. I can't imagine what we would instead have without the "quadratic forms" you mentioned, maybe tons of summations and dot dot dots? May I suggest that you embrace these notations with a leap of faith then re-evaluate their usefulness after you are familiar with them? – Ye Tian Mar 4 at 5:16