R: Range Space

orth {pracma} | R Documentation

## Range Space

### Description

Range space or image of a matrix.

### Usage

    orth(M)

### Arguments

`M` | Numeric matrix; vectors will be considered as column vectors.

### Details

`B=orth(A)` returns an orthonormal basis for the range of `A`. The columns of `B` span the same space as the columns of `A`, and the columns of `B` are orthogonal to each other.

The number of columns of `B` is the rank of `A`.

### Value

Matrix of orthogonal columns, spanning the image of `M`.

### References

Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Philadelphia.

### See Also

`nullspace`

### Examples

    M <- matrix(1:12, 3, 4)
    Rank(M)                 #=> 2
    orth(M)

[Package pracma version 2.0.4 Index]