24.3 Properties and Attibutes of Matrices

is a list of length 2, the first being the number of rows, the second being the number of columns of the matrix mat.

gap> DimensionsMat([[1,2,3],[4,5,6]]);
[ 2, 3 ]

For a matrix mat, DefaultFieldOfMatrix returns either a field (not necessarily the smallest one) containing all entries of mat, or fail.

If mat is a matrix of finite field elements or a matrix of cyclotomics, DefaultFieldOfMatrix returns the default field generated by the matrix entries (see Creating Finite Fields and Operations for Cyclotomics).

gap> DefaultFieldOfMatrix([[Z(4),Z(8)]]); 
GF(2^6)

The trace of a square matrix is the sum of its diagonal entries.

gap> TraceMat([[1,2,3],[4,5,6],[7,8,9]]);
15

returns the determinant of the square matrix mat

Does the same as DeterminantMat, with the difference that it may destroy its argument. The matrix mat must be mutable.

gap> DeterminantMat([[1,2],[2,1]]);
-3
gap> mm:= [[1,2],[2,1]];;
gap> DeterminantMatDestructive( mm );
-3
gap> mm;
[ [ 1, 2 ], [ 0, -3 ] ]

A matrix is monomial if and only if it has exactly one nonzero entry in every row and every column.

gap> IsMonomialMatrix([[0,1],[1,0]]);
true

returns true if mat has only zero entries off the main diagonal, false otherwise.

returns true if mat has only zero entries below the main diagonal, false otherwise.

returns true if mat has only zero entries below the main diagonal, false otherwise.

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