R: Matrix Norm

norm {fBasics} | R Documentation

## Matrix Norm

### Description

Returns the norm of a matrix.

### Usage

    norm2(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. `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.

### 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.

Note, the function `fBasics::norm()` has become obsolete, since `base::norm()` has become available in the R base environment. To avoid conflicts with `norm()` we have renamed in the fBasics package as `norm2`.

### Value

returns the value of the norm 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)

[Package fBasics version 3042.89 Index]