matrix-norm: Matrix norm

In fBasics: Rmetrics - Markets and Basic Statistics

Matrix norm

Description

Computes the norm of a matrix.

Usage

norm2(x, p = 2)

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.

Value

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

Note

Since base::norm() has become available in the R base environment, the function fBasics::norm() has become obsolete. To avoid conflicts with norm() we have renamed the fBasics' one to norm2.

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)                                                       

fBasics documentation built on Sept. 11, 2024, 6:34 p.m.