A basis for the null space of the matrix A, i.e. the solution of AX=0
is found by the command
MAT SOLVE X FROM A*X=0
This is done by the singular value decomposition A=UDV' and taking
the basis X of the null space as the columns of V corresponding to
singular values = 0 (< 1e-15). The tolerance value (1e-15) can be
changed by a specification EPS=<value>.
An alternative operation is
MAT X=NULL(A).
MAT SOLVE <X> FROM <A>*<X>=<B>
where A is m*n, m>=n and r(A)=n,
B is m*k
yields the solution X of linear equations (when m=n)
or the least squares solution X (when m>n).
The algorithm is automatically selected according to the nature of A:
If A is diagonal, solution is trivial,
else if A is triangular, straight backsubstitution is used,
else if A is symmetric, 'choldet1' and 'cholsol1' is used,
else (when m>=n) 'Ortholin1' is used.
If the columns of A are linearly dependent, an error message will be
displayed. eps=1e-15 is the tolerence limit for 'non-zero' entities.
In this case the singular value decomposition may be used (see SING).
Reference: Wilkinson-Reinsch: Handbook for Automatic Computation,
Vol.II, Linear algebra.
N = Solving AX=0 (Finding null space of A)
M = More information on MAT operations