Page 22, Lemma 1.7, part 2: This is imprecise on which norms I mean.
There are 3 norms in the inequality "||A*B|| <= ||A|| * ||B||", and
not every choice of 3 norms makes sense. The easiest case is when
A and B are square, and you use the same vector norm in the numerator
and denominator of definition 1.9 for all 3 norms. This is all I wanted
you to prove for Question 1.16. (Hyounjin Kim)
The result is
more generally true as long as you use the same norm for the vectors
in the domain space of A*B and B, the same norm for vectors
in the range space of B and the domain space of A, and the same norm
for vectors in the range space of A*B and the range of A. In other
words, you can choose three different vector norms.