# norm {Matrix}

Matrix Norms
Package:
Matrix
Version:
1.0-12

### Description

Computes a matrix norm of `x`, using Lapack for dense matrices. The norm can be the one norm, the infinity norm, the Frobenius norm, or the maximum modulus among elements of a matrix, as determined by the value of `type`.

### Usage

```norm(x, type, ...)
```

### Arguments

x
a real or complex matrix.
type
A character indicating the type of norm desired.
`"O"`, `"o"` or `"1"`
specifies the one norm,     (maximum absolute column sum);
`"I"` or `"i"`
specifies the infinity norm (maximum     absolute row sum);
`"F"` or `"f"`
specifies the Frobenius norm (the     Euclidean norm of `x` treated as if it were a vector); and
`"M"` or `"m"`
specifies the maximum modulus of     all the elements in `x`.

The default is `"O"`. Only the first character of `type[1]` is used.

...
further arguments passed to or from other methods.

### Details

For dense matrices, the methods eventually call the Lapack functions `dlange`, `dlansy`, `dlantr`, `zlange`, `zlansy`, and `zlantr`.

### Values

A numeric value of class `"norm"`, representing the quantity chosen according to `type`.

### References

Anderson, E., et al. (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia.

### Examples

```x <- Hilbert(9)
norm(x, "1")
norm(x, "I")
norm(x, "F")
norm(x, "M")```

Documentation reproduced from package Matrix, version 1.0-12. License: GPL (>= 2)