NULLSPACE _ _ _ _ _ _ _ _ _ _ _ _ operator

syntax:

<nullspace> calculates for its matrix argument, a, a list of linear independent vectors (a basis) whose linear combinations satisfy the equation a x = 0. The basis is provided in a form such that as many upper components as possible are isolated.

examples:

nullspace mat((1,2,3,4),(5,6,7,8)); 


         {
           [ 1  ]
           [    ]
           [ 0  ]
           [    ]
           [ - 3]
           [    ]
           [ 2  ]
           ,
           [ 0  ]
           [    ]
           [ 1  ]
           [    ]
           [ - 2]
           [    ]
           [ 1  ]
          }

Note that with b := nullspace a, the expression lengt h b is the nullity/ of A, and that second length a - length b calculates the rank/ of A. The rank of a matrix expression can also be found more directly by the rank operator.

In addition to the REDUCE matrix form, nullspace accepts as input a matrix given as a list of lists, that is interpreted as a row matrix. If that form of input is chosen, the vectors in the result will be represented by lists as well. This additional input syntax facilitates the use of nullspace in applications different from classical linear algebra.