endomorphism's Usage Examples:

In mathematics, an endomorphism is a morphism from a mathematical object to itself.

An endomorphism that is also an isomorphism is an automorphism.

algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic.

endomorphisms of an abelian group X form a ring.

This ring is called the endomorphism ring X, denoted by End(X); the set of all homomorphisms of X into itself.

a lattice endomorphism is a lattice homomorphism from a lattice to itself, and a lattice automorphism is a bijective lattice endomorphism.

In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.

homomorphism that sends an invertible n-by-n matrix g {\displaystyle g} to an endomorphism of the vector space of all linear transformations of R n {\displaystyle.

elliptic curves over a field of characteristic p > 0 with unusually large endomorphism rings.

Building on the previous example, given a section s of an endomorphism bundle Hom(E, E) and a function f: X → R, one can construct an eigenbundle.

In category theory, an automorphism is an endomorphism (i.

F is algebraically closed, every endomorphism of Fn has some eigenvector.

On the other hand, if every endomorphism of Fn has an eigenvector, let p(x).

In the case when M = R the endomorphism ring EndR(R) = R, where each endomorphism arises as left multiplication by a fixed ring element.

characteristic 0, or, when k has characteristic p > 0, the Frobenius endomorphism x ↦ xp is an automorphism of k.

with identical source and target) is an endomorphism of X.

A split endomorphism is an idempotent endomorphism f if f admits a decomposition f = h ∘ g.

where V = W {\displaystyle V=W} , a linear map is called a (linear) endomorphism.

polynomial of an endomorphism of vector spaces of finite dimension is the characteristic polynomial of the matrix of the endomorphism over any base; it.

That notion corresponds to matrices representing the same endomorphism V → V under two different choices of a single basis of V, used both for.

In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number.