Subsections

• Arithmetic
• Predicates

Sum of the matrices a and b, where a and b belong to a common matrix algebra R.

a + t : AlgMatElt, RngElt -> AlgMatElt

t + a : AlgMatElt, RngElt -> AlgMatElt

Sum of the matrix a and the scalar matrix t * I.

Negation of the matrix a.

a - b : AlgMatElt, AlgMatElt -> AlgMatElt

Difference of the matrices a and b, where a and b belong to the same matrix algebra R.

a - t : AlgMatElt, RngElt -> AlgMatElt

t - a : AlgMatElt, RngElt -> AlgMatElt

Difference of the matrix a and the scalar matrix t * I.

Product of the matrices a and b, where a and b belong to the same matrix algebra R.

a * b : AlgMatElt, ModHomElt -> ModHomElt

Given a matrix a belonging to a subalgebra of M_n(S) and an element b of a submodule of Hom(R^((n)), R^((m))), construct the product of a and b as an element of Hom(R^((n)), R^((m))).

a * b : ModHomElt, AlgMatElt -> ModHomElt

Given a matrix a belonging to a submodule of Hom(R^((n)), R^((m))) and an element b of a subalgebra of M_m(S), construct the product of a and b as an element of Hom(R^((n)), R^((m))).

t * a : RngElt, AlgMatElt -> AlgMatElt

a * t : AlgMatElt, RngElt -> AlgMatElt

Given an element a of the matrix algebra R, and an element t belonging to the coefficient ring S of R, form their scalar product.

u * a : ModTupElt, AlgMatElt -> ModTupElt

Given an element u belonging to the S-module S^((n)) and an element a belonging to a subalgebra of M_n(S), form the element u * a of S^n.

If n is positive, form the n-th power of a; if n is zero, form the identity matrix; if n is negative, form the ( - n)-th power of the inverse of a.

Ncols(a) : AlgMatElt -> RngIntElt

The number of columns in the matrix a.

Nrows(a) : AlgMatElt -> RngIntElt

The number of rows in the matrix a.

Sections

• Comparison
• Properties of Elements

True if the matrix a is equal to the matrix b, where a and b are elements of a common matrix algebra R.

True if the matrix a is not equal to the matrix b, where a and b are elements of a common matrix algebra R.

True iff the element a belonging to the matrix algebra R is a diagonal matrix; i.e. the only non-zero entries are on the diagonal.

True iff the element a belonging to the matrix algebra R is the negation of the identity element for R.

True iff the element a belonging to the matrix algebra R is the identity element for R.

True iff the element a belonging to the matrix algebra R is a scalar matrix.

True iff the element a belonging to the matrix algebra R is a symmetric matrix; i.e. the transpose of a equals a.

True iff the matrix a belonging to the matrix algebra R is a unit.

True iff the element a belonging to the matrix algebra R is the zero element for R.