Definitions for contragredient
con·tra·gre·di·ent

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1. contragredientadjective

   Generally, an object contragredient to another is the object inversed and transposed.

2. contragredientadjective

   A contragredient representation in linear algebra is the transpose of the former representation of an inverse object.

3. contragredientadjective

   A contragredient matrix is a transpose of an inverse matrix.

4. 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.

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1. 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.

How to pronounce contragredient?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say contragredient in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of contragredient in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of contragredient in Pythagorean Numerology is: 9

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Contragredient
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Contragredient