The class is for square matrix whose coefficient ring belongs ring. It is a subclass of RingMatrix, SquareMatrix and ring.ringElement.
row and column must be a positive integer and row has to equal column.
compo must be a list form.
coeff_ring must be an instance of ring.Ring.
In general, given matrix size and coefficient ring unspecified, you should call createMatrix for your profit.
Change the class of the matrix to FieldSquareMatrix, where the coefficient ring will be the quotient field of the current domain. It overrides the method from RingMatrix.
Return the MatrixRing instance.
Check whether self is orthogonal matrix or not.
Check whether self is alternating matrix or not.
Check whether self is singular matrix or not.
Return the trace.
Return the determinant.
Return the (i, j)-cofactor.
Return the commutator defined as [M, N] = M * N - N * M .
Return the characteristic matrix.
Return the characteristic polynomial.
Return the adjugate matrix, i.e. adj(M) s.t. M * adj(M) = adj(M) * M = det(M) * E .
Return the cofactor matrix.
Compute Smith normal form(SNF) for nonsingular matrix, and return the list of diagonal elements.
Ex.
>>> A = matrix.RingSquareMatrix(3, [87,38,80]+[13,6,12]+[65,28,60]) >>> A.smithNormalForm() [4L, 2L, 1L]
Compute Smith normal form M and U,V satified U*self*V=M, and return RingSquareMatrix tuple (U,V,M).
operator | explanation |
M ** c | Return the c-th power of matrices M. |