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Exercise 2.1.17 (a) Let A be a positive definite matrix, and let R be its Cholesky factor, so that A = RT R. Verify

Exercise 2.1.17 (a) Let A be a positive definite matrix, and let R be its Cholesky factor, so that A RTR. Verify that for all ER IlzIIA Il Rar (b) Using the fact that the 2-norm is indeed a norm on R, prove that the A-norm is a norm on R 

Exercise 2.1.17 (a) Let A be a positive definite matrix, and let R be its Cholesky factor, so that A = RT R. Verify that for all x E R", || x || A = || Rx ||2. (b) Using the fact that the 2-norm is indeed a norm on R", prove that the A-norm is a norm on R".

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