# norm

Norm of a vector or matrix

### norm(x)

• If x is a vector, it returns the 2-norm of x, i.e., $$||x||_2=\sqrt{x_1^2+x_2^2+\cdots+x_n^2}$$

### norm(x, p)

• If x is a vector, p should be positive infinity, negative infinity, or a positive scalar.
• If p is positive infinity, it returns the largest absolute value of x's elements.
• If p is negative infinity, it returns the smallest absolute value of x's elements.
• Otherwise, it returns the p-norm of x, i.e., $$||x||_p=\left(|x_1|^p+|x_2|^p+\cdots+|x_n|^p\right)$$

• If x is a matrix, p should be either 1, 2, or infinity.

• If p is 1, it returns (assuming m rows and n columns) $$\max_{j\in{1,2,\ldots,n}} \sum^m_{i=1}|x_{ij}|.$$

• If p is 2, it returns the largest singular value of x.

• If p is inf, it returns (assuming m rows and n columns) $$\max_{i\in{1,2,\ldots,m}} \sum^n_{j=1}|x_{ij}|.$$