`myorth(X)`

makes an orthonormal basis for the space spanned by the columns of `X`

. The number of columns returned equals `myrank(X)`

, which is the rank of `X`

.

1 2 |

`X` |
numeric matrix. |

`tol_` |
tuning parameter for the rank. |

The calculations are based on the singular value decomposition (`svd`

). And `myrank(X)`

is the number of singular values of `X`

that are larger than `max(dim(X))*svd(x)$d[1]*tol_`

.

`myorth`

returns a matrix, whose columns form an orthonormal
basis.

`myrank`

returns a single number, which is the rank of `X`

.

In the special case where `X`

has a single column, `myorth(X)`

returns `c*X`

where `c`

is a positive constant.

Øyvind Langsrud and Bjørn-Helge Mevik

`svd`

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