This problem investigates how some norm values compare with the maximum of the absolute values of all matrix entries, that can be computed using the MATLAB command max(max(abs  For  build matrices and...

This problem investigates how some norm values compare with the maximum of the absolute values of all matrix entries,

that can be computed using the MATLAB command max(max(abs For
 build matrices

and compute

What is the apparent relationship between

and the matrix norms? Prove your assertion. Hint: For the induced norms, assume

occurs at indices

<sub>max

max</sub>
 By definition

If

_k
is a standard basis vector, then

<sub>k

k

k</sub>