fBasics (version 4032.96)

norm: Matrix norm

Description

Computes the norm of a matrix.

Usage

norm2(x, p = 2)

Value

the requested norm of the matrix, a non-negative number

Arguments

x

a numeric matrix.

p

an integer value, 1, 2 or Inf, see section ‘Details’.

Details

The function norm2 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:                      
   norm2(P)