A subspace is cyclic if it is generated by the action of exactly one of these functions an element of the subspace.
The product of the elementary divisors of one of these mathematical objects is equal to its minimal polynomial if it is nonderogatory. The multiset of elementary divisors is invariant for similar ones, where similarity is defined as an equivalence class under conjugation by an automorphism in GL. When the codomain is a field, these functions are one-forms. A subspace is cyclic if it is generated by the action of exactly one of these functions an element of the subspace. These maps are the (*) endomorphisms of vector spaces since they distribute over addition and scalar multiplication. The set of all vectors that one of these maps to zero is the nullspace. For 10 points, identify these maps which, in the case of a finite-dimensional domain and codomain, can be represented by matrix multiplication.
The product of the elementary divisors of one of these mathematical objects is equal to its minimal polynomial if it is nonderogatory.
linear mappings [or linear operators; or linear transformations; accept linear functions; accept just linear after "functions" is read; prompt on "matrices" before "matrix" is read]