pracma (version 0.5-3)

orth: Range Space

Description

Range space or image of a matrix.

Usage

orth(M)

Arguments

M

Numeric matrix; vectors will be considered as column vectors.

Value

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

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.

References

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

See Also

nullspace

Examples

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