Using Cholesky and Exercise 3.2, write a subroutine to compute the inverse of a positive definite matrix. Can it be done using only the n(n +1)/2 storage locations in symmetric storage mode? Prove...

Using Cholesky and Exercise 3.2, write a subroutine to compute the inverse of a positive definite matrix. Can it be done using only the n(n +1)/2 storage locations in symmetric storage mode?

Prove that A2 = (largest eigenvalue of AT A)1/2. Also show that the condition number of the matrix A based on the p = 2 norm κ2(A) is the square root of the ratio of the largest and smallest eigenvalues of AT A.