by **Guest** » Mon Nov 30, 2020 2:13 pm

I am puzzled by this. You say you know the definitions. This matrix, a diagonal matrix with the same number, "k", on the diagonal, is a particularly trivial matrix!

You know that [tex]||A||_1= max \sum_i |a_{ij}|[/tex]. That sum is over each column but since each column has one k and n-1 0s each sum is just k and the maximum is k.

[tex]||A||_\infty[/tex], conversely, the maximum of the sums over the rows but, again, every row sum is k so the maximum is k.

[tex]||A||_2[tex] is the absolute value of the largest eigenvalue. The diagonal matrix with "k"s on the diagonal has all eigenvalues k so the largest eigenvalue is k. This norm is, again, k.