fBasics (version 2110.79)

norm: Matrix Norm

Description

Returns the norm of a matrix.

Usage

norm(x, p = 2)

Arguments

x

a numeric matrix.

p

an integer value, 1, 2 or Inf. p=1 - The maximum absolute column sum norm which is defined as the maximum of the sum of the absolute valued elements of columns of the matrix.

Details

The function norm computes the norm of a matrix. Three choices are possible: p=1 - The maximum absolute column sum norm which is defined as the maximum of the sum of the absolute valued elements of columns of the matrix. p=2 - The spectral norm is "the norm" of a matrix X. This value is computed as the square root of the maximum eigenvalue of CX where C is the conjugate transpose. p=Inf - The maximum absolute row sum norm is defined as the maximum of the sum of the absolute valued elements of rows of the matrix.

References

Golub, van Loan, (1996); Matrix Computations, 3rd edition. Johns Hopkins University Press.

Examples

## Create Pascal Matrix:
   P = pascal(5)
   P                  
     
## Return the Norm of the Matrix:                      
   norm(P)