### The Maxima on-line user's manual

Algebra Calculator

#### Columnspace

Function: columnspace (<M>) If <M> is a matrix, return `span (v_1, ..., v_n)`, where the set `{v_1, ..., v_n}` is a basis for the column space of <M>. The span of the empty set is `{0}`. Thus, when the column space has only one member, return `span ()`.

```(%o1)                                true
(%i2) ```

### Related Examples

##### columnspace-matrix

m:matrix([1,2,3],[2,5...

columnspace(m);

Calculate

##### columnspace-matrix

m:matrix([1,2,5,-3],[...

columnspace(m);

Calculate

##### columnspace-matrix-transpose

a: matrix ([4,1,-1], ...

columnspace(transpose...

Calculate

? columnspace;

Calculate

##### columnspace-matrix

m:matrix([9,5,-4,2],[...

columnspace(m);

Calculate

##### columnspace-matrix

m:matrix([1,1],[-1,-1]);

columnspace(m);

Calculate

##### columnspace-matrix-triangularize

A:matrix([7,0,1,3,2],...

B:triangularize(A);

columnspace(B);

Calculate

##### columnspace-matrix

m:matrix([9,5,-4,2],[...

columnspace(m);

Calculate

##### columnspace-matrix

m:matrix([1,2,3],[2,5...

columnspace(m);

Calculate

##### columnspace-matrix-nullspace

m:matrix([15,9,-3,9],...

nullspace(m);

columnspace(m);

Calculate