Matrix Norms

Let . A norm of is denoted by .

Definitions

Suppose for all the definitions below.

1-norm

Maximum of the absolute column sums.

2-norm

Square root of the sum of all elements squared. Also called as Euclidean norm.

Infinity norm

Maximum of the row sums.

Vector norm

Norm defined for column vectors.

Properties of Norms

Works for all types of norms.

Suppose are ordered.

4. (triangle inequality)