Problem 8 - To define conditioning, we first need to define matrix norms. For now, you can consider a norm as an operato

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Problem 8 To Define Conditioning We First Need To Define Matrix Norms For Now You Can Consider A Norm As An Operato 1 (35.32 KiB) Viewed 48 times

Problem 8 - To define conditioning, we first need to define matrix norms. For now, you can consider a norm as an operator ||-|| Rnxn R. That means, the operator takes in an n x n matrix, and returns a single real number. Intuitively, you can think of norms as describing the "length" of a matrix. Consider the co-norm given by: ||A|| = max Isisn j= 1. Determine the co-norm of the following matrix: A 2-1 Aigl 2. A condition number represents how susceptible a matrix is to roundoff errors. Let the condition number of a matrix A using x-norm is defined by || A||-|| A||. Find the condition number of the following matrix, where 0 << 1: A = - (19) 3. Explain what happens to the condition number when € varies.