Hello, I need help with problem number 1. Attached will be the example of the L-1 norm and brief explanation for the L-inf norm. What I can't seem to grasp is why the matrix norm is the "maximum column sum"or "maximum row sum" for the L-1 or L-inf norm respectively. Essentially I haven't connected yet in mathematical notation how the matrix norm of L-1 is "maximum column sum" and further for the L-inf norm.

Problem 1: Consider the vector space X = U\" with the Em-norm \"X\" = maxlril. What is the corresponding induced norm of a matrix? Hint: We solved this problem in class for the El norm. The argument for the 80 norm is very similar. Example 3.3. The 1-Norm of a Matrix. If A is any m x n matrix, then |All is equal to the "maximum column sum" of A. We explain and derive LECTURE 3. NORMS 21 this result as follows. Write A in terms of its columns A = al an (3.8) where each a; is an m-vector. Consider the diamond-shaped 1-norm unit ball in C", illustrated in (3.2). This is the set {x e C" : Eh, (x,