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| KASH3 Reference Manual

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### Keyword

Matrices

### Description

<shortdoc> To construct a matrix first we need a ring from which are the coefficients. For example Q,R and C are predefined for the rational, real and complex numbers. We can also build matrices over function or number fields. Then we need also the number of rows and columns and finitely a list consisting of the entries.We can compute the kernel N of a matrix M (as a matrix which islinear map in the kernel of M) or the Nullspace of N. </shortdoc>

### Examples

k := RationalFunctionField(FiniteField(5,2)); P := PolynomialAlgebra(k); F := FunctionField(P.1^3 + k.1^3 + k.1 + 1); M := Matrix(F, 2,2, [ F.1+k.1, 2, F.1+k.1,2]);
N := Matrix(Q, 2,3, [1,2,3,5,0,1]); KernelMatrix(N); w := KernelMatrix(Transpose(N)); N*Transpose(w); v := Transpose(Matrix(Q, 3,1, [1,2,3])); Solution(N,v);
T := Matrix(Q, 2,2,[1,2,1,2]); KernelMatrix(T);

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