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Module Homomorphisms

Homomorphisms of AbstractAlgebra modules, $f : R^s \to R^t$, can be represented by $s\times t$ matrices over $R$.

AbstractAlgebra.Generic.ModuleHomomorphism — Method.
ModuleHomomorphism(M1::AbstractAlgebra.Module{T}, M2::AbstractAlgebra.Module{T}, m::AbstractAlgebra.MatElem{T}) where T <: RingElement

Create the homomorphism $f : M_1 \to M_2$ represented by the matrix $m$.

Examples

M = FreeModule(ZZ, 2)
f = ModuleHomomorphism(M, M, matrix(ZZ, 2, 2, [1, 2, 3, 4]))

m = M([ZZ(1), ZZ(2)])

f(m)