ColumnSpaceBasis
Finds a basis for the column space of a matrix.
Syntax
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ColumnSpaceBasis(A)-
Ais a matrix
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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⎠