Algosim documentation: ColumnSpaceBasis

ColumnSpaceBasis

Finds a basis for the column space of a matrix.

Syntax

Description

If A is a matrix, not necessarily square, then ColumnSpaceBasis(A) is a matrix whose columns form a basis for the column space of A. Hence, ColumnSpaceBasis(A) might be obtained by selectively removing superfluous columns from A (but it is not guaranteed that every column in ColumnSpaceBasis(A) is one of the columns of A).

Examples

A ≔ ❨❨2, 2, −5, 0, −1❩, ❨1, 5, −2, 1, 5❩, ❨0, 1, 3, 2, 6❩, ❨−2, 1, 4, 6, 9❩, ❨3, −2, 7, −2, 6❩❩
⎛ 2   2  −5   0  −1⎞
⎜ 1   5  −2   1   5⎟
⎜ 0   1   3   2   6⎟
⎜−2   1   4   6   9⎟
⎝ 3  −2   7  −2   6⎠
ColumnSpaceBasis(A)
⎛ 2   2  −5   0⎞
⎜ 1   5  −2   1⎟
⎜ 0   1   3   2⎟
⎜−2   1   4   6⎟
⎝ 3  −2   7  −2⎠

See also