Run an experiment like that in to formulate a good guess for the value of the matrix norm Experimentally estimate ∞ for two matrices. Notice that in Example 7.6, the experimental results using matrix...

Run an experiment like that in

to formulate a good guess for the value of the matrix
norm

Experimentally estimate ∞ for two matrices.

Notice that in Example 7.6, the experimental results using matrix
indicate an actual value of 9.0, which is the sum of the absolute value of the entries in row 1. For matrix

the experiment indicates that the norm is the sum of the absolute values of the entries in row 2. In fact, here is the way to compute
_∞
for any
matrix. Find the sum of the absolute values of the elements in each row of

and take

_∞
be the maximum of these sums; in other words

How do we get from the definition of the infinity-induced matrix norm

to this simple expression? Theorem 7.4 answers that question. The proof is somewhat technical, and is here for the interested reader.