Suppose A in C

m$\backslash$times n

$.$ Consider the matrix norm kAk induced by the two vector $1-$norms kxk$1$

and kyk$1$ for x in C

n and y in C

m respectively,

kAk $=$ max

kxk$1=1$

kAxk$1.$

Is this induced norm the same as the matrix $1-$norm defined by

kAk$1=$ max

$1<=$i$<=$n

kAeik$1?$

If so prove it$.$ If not give counterexample to disprove it$.$