The norm of a real vector or matrix.

Syntax

n = Norm(X, p)

n = Norm(X, char)

Arguments

Name

Description

X

A real vector or matrix.

p

A positive integer specifying the p Norm. The default is 2.

char

Either ‘inf’, ‘-inf’ or ‘fro.’

Outputs

Name

Description

n

The norm of X.

Example 1

Find the norm of the vector [3, 4].

Syntax

n = Norm([3, 4])

Results

n = 5

Example 2

Find the norm of the matrix [4, 0; 0, 3]

Syntax

n = Norm([4, 0; 0, 3])

Results

n = 4

Comments

char = ‘inf’ returns the largest value of X in the absolute value.

char = ‘-inf’ returns the smallest value of X in absolute value (only for vectors).

char = ‘fro’ returns the Frobenius norm of X, which is the square root of the sum of the squared values.

p = 1 returns the sum of the absolute values.

p = 2 returns the Euclidean norm (or length) of a vector, and the largest singular value of a matrix.

p > 2 returns the p norm of a vector.

See Also:

Cond