A matrix norm is a function that assigns a strictly positive number to a non-zero matrix, representing its "size" or "magnitude".

L1 Norm (Maximum Column Sum):

\( \|A\|_1 = \max_{j} \sum_{i=1}^{m} |a_{ij}| \)

This is found by summing the absolute values of the elements in each column, and then taking the largest of those sums.

Infinity Norm (Maximum Row Sum):

\( \|A\|_\infty = \max_{i} \sum_{j=1}^{n} |a_{ij}| \)

This is found by summing the absolute values of the elements in each row, and then taking the largest of those sums.

Frobenius Norm:

\( \|A\|_F = \sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n} |a_{ij}|^2} \)

This is the square root of the sum of the squares of all elements in the matrix.