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November 27th, 2016, 02:43 PM   #1
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From: Pasay

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Matrix property?

Let A be an m x n matrix. Show that the matrix $A^{T}A$ has the property that $x^{T}(A^{T}A)≥ 0$ for every $x ∈ R^{n}$.


How do I start to prove this? I tried doing this:
$x^{T}(A^{T}A) ≥ 0$
$(Ax)^{T}A ≥ 0$
But, I got stuck because this doesn't show $A^{T}A$ to be positive.


Help is greatly appreciated, thank you.
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