isomorphic's Usage Examples:

Two mathematical structures are isomorphic if an isomorphism exists between them.

infinite cyclic group is isomorphic to the additive group of Z, the integers.

Every finite cyclic group of order n is isomorphic to the additive group of.

A set of graphs isomorphic to each other is called an isomorphism class of graphs.

The two graphs shown below are isomorphic, despite their different.

between two groups, then the groups are called isomorphic.

From the standpoint of group theory, isomorphic groups have the same properties and need not.

{\displaystyle F} and G {\displaystyle G} are called naturally isomorphic or simply isomorphic if there exists a natural isomorphism from F {\displaystyle.

The dual of M is isometrically isomorphic to X ′ / M ⊥.

The dual of X / M {\displaystyle X/M} is isometrically isomorphic to M ⊥.

homomorphism is always isomorphic to a quotient of G.

Specifically, the image of G under a homomorphism φ: G → H is isomorphic to G / ker(φ) where ker(φ).

{\textstyle n} , then End ⁡ ( V ) {\textstyle \operatorname {End} (V)} is isomorphic to the associative algebra of all n × n {\textstyle n\times n} matrices.

Loosely speaking, a direct sum is isomorphic to a weak direct product of subgroups.

An isomorphic keyboard is a musical input device consisting of a two-dimensional grid of note-controlling elements (such as buttons or keys) on which any.

Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that.

geometries, since any finite projective space of dimension three or greater is isomorphic to a projective space over a finite field (that is, the projectivization.

all abelian groups of order 15 are isomorphic.

For another example, every abelian group of order 8 is isomorphic to either Z 8 {\displaystyle \mathbb.

(UK: /ˈkɜːbnər/, US: /ˈkɛb-/), also called the Koebner response or the isomorphic response, attributed to Heinrich Köbner, is the appearance of skin lesions.

Pairs (n, eH) form a normal subgroup isomorphic to N, while pairs (eN, h) form a subgroup isomorphic to H.

Orientation-preserving isometries of the Poincaré half-plane, isomorphic to SU(1,1), isomorphic to Sp(2,R).

implies the statement that if two Lie groups are isomorphic as topological groups, then they are isomorphic as Lie groups.

(or first isomorphism theorem) states that image of a homomorphism is isomorphic to the quotient by the kernel.

are naturally isomorphic as vector spaces, but with different multiplications (in the case of characteristic two, they are still isomorphic as vector spaces.

isomorphism, and the rings R and S are called isomorphic.

From the standpoint of ring theory, isomorphic rings cannot be distinguished.

Synonyms:

isomorphous;