- In mathematics, an
endomorphism is a
morphism from a
mathematical object to itself. An
endomorphism that is also an
isomorphism is an automorphism. For...
-
algebra and
field theory, the
Frobenius endomorphism (after
Ferdinand Georg Frobenius) is a
special endomorphism of
commutative rings with
prime characteristic...
-
under consideration. The
endomorphism ring
consequently encodes several internal properties of the object. As the
endomorphism ring is
often an algebra...
- of
prime characteristic p, R → R, x → xp is a ring
endomorphism called the
Frobenius endomorphism. If R and S are rings, the zero
function from R to S...
- case
where V = W {\displaystyle V=W} , a
linear map is
called a
linear endomorphism.
Sometimes the term
linear operator refers to this case, but the term...
- In
linear algebra, the
trace of a
square matrix A,
denoted tr(A), is the sum of the
elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...
- a
lattice endomorphism is a
lattice homomorphism from a
lattice to itself, and a
lattice automorphism is a
bijective lattice endomorphism.
Lattices and...
- E. In the case when M = R (****umed unital), the
endomorphism ring EndR(R) = R,
where each
endomorphism arises as left
multiplication by a
fixed ring element...
-
point of
category theory. A
homomorphism may also be an isomorphism, an
endomorphism, an automorphism, etc. (see below). Each of
those can be
defined in a...
-
determinant of a
linear endomorphism determines how the
orientation and the n-dimensional
volume are
transformed under the
endomorphism. This is used in calculus...
