What does contragredient mean?
Definitions for contragredient
con·tra·gre·di·ent
This dictionary definitions page includes all the possible meanings, example usage and translations of the word contragredient.
Wiktionary
contragredientadjective
Generally, an object contragredient to another is the object inversed and transposed.
contragredientadjective
A contragredient representation in linear algebra is the transpose of the former representation of an inverse object.
contragredientadjective
A contragredient matrix is a transpose of an inverse matrix.
Etymology: Neologism based on the English prefix contra- and gredient. Gredient may be based on the English word grid, since the mathematical objects referred to as contragredient are often represented as grids of numbers.
Wikipedia
contragredient
In algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring R, then a function f : M → N {\displaystyle f:M\to N} is called an R-module homomorphism or an R-linear map if for any x, y in M and r in R, f ( x + y ) = f ( x ) + f ( y ) , {\displaystyle f(x+y)=f(x)+f(y),} f ( r x ) = r f ( x ) . {\displaystyle f(rx)=rf(x).} In other words, f is a group homomorphism (for the underlying additive groups) that commutes with scalar multiplication. If M, N are right R-modules, then the second condition is replaced with f ( x r ) = f ( x ) r . {\displaystyle f(xr)=f(x)r.} The preimage of the zero element under f is called the kernel of f. The set of all module homomorphisms from M to N is denoted by Hom R ( M , N ) {\displaystyle \operatorname {Hom} _{R}(M,N)} . It is an abelian group (under pointwise addition) but is not necessarily a module unless R is commutative. The composition of module homomorphisms is again a module homomorphism, and the identity map on a module is a module homomorphism. Thus, all the (say left) modules together with all the module homomorphisms between them form the category of modules.
Numerology
Chaldean Numerology
The numerical value of contragredient in Chaldean Numerology is: 6
Pythagorean Numerology
The numerical value of contragredient in Pythagorean Numerology is: 9
Translations for contragredient
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"contragredient." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/contragredient>.
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