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