Let S be a positive definite n x n matrix. For any x in E" define
Chapter 7, Problem 15(choose chapter or problem)
Let S be a positive definite n x n matrix. For any x in E" define ||x|| = (x'Sx)1 ' 2 . Show that this defines a norm on R". [Hint: Use the Cholesky factorization of S to show that x'Sy = y'Sx < (x'Sx)1/2 (y'Sy)1/2.]
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