Question: Let S be a positive definite n n matrix. For any x in Rn define ||x|| = (xtSx)1/2. Show that this defines a norm

Let S be a positive definite n × n matrix. For any x in Rn define ||x|| = (xtSx)1/2. Show that this defines a norm on Rn. [Use the Cholesky factorization of S to show that xtSy = ytSx ≤ (xtSx)1/2(ytSy)1/2.]

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