linalg::nullspace
-- basis for
the null space of a matrixlinalg::nullspace
(A)
returns a basis for
the null space of the matrix A, i.e., a list B of
linearly independent vectors such that A*x=0 if and only if
x is a linear combination of the vectors in
B.
linalg::nullspace(A)
A |
- | a matrix of a domain of category Cat::Matrix |
a list of (column) vectors of the domain Dom::Matrix(R)
, where R
is
the component ring of A
.
linalg::basis
,
linalg::matlinsolve
, linsolve
, numeric::matlinsolve
A
must be a field,
i.e., a domain of category Cat::Field
.A
does not have a canonical
representation of the zero element, it can happen that
linalg::nullspace
does not find a basis for the null
space. In such a case, a wrong result is returned.The kernel of the matrix:
>> A := Dom::Matrix(Dom::Real)( [[3^(1/2)*2 - 2, 2], [4, 3^(1/2)*2 + 2]] )
+- -+ | 1/2 | | 2 3 - 2, 2 | | | | 1/2 | | 4, 2 3 + 2 | +- -+
is one-dimensional, and a basis is {[-1/(sqrt(3)-1),1]}:
>> linalg::nullspace(A)
-- +- -+ -- | | 1 | | | | - -------- | | | | 1/2 | | | | 3 - 1 | | | | | | | | 1 | | -- +- -+ --
linalg::nullSpace