# moodul (3)

olemus
algebraline süsteem, mis koosneb vektoritest ja skalaaridest
= a generalization of a vector space

Wiktionary:
6. (algebra, ring theory) an abelian group equipped with the operation of multiplication by an element of a ring (or another of certain algebraic objects), representing a generalisation of the concept of vector space with scalar multiplication

- vektoreid saab selles liita ja skalaariga korrutada
- liitmise suhtes on Abeli rühm
- skalaaride a, b ja vektorite x, y vahel kehtivad seosed:
a(bx) = (ab)x
1x = x
(a + b)x = ax + bx
a(x + y) = ax + ay

näide
iga aditiivne Abeli rühm, kui skalaarideks on täisarvude hulk

ülevaateid
https://mathworld.wolfram.com/Module.html

https://en.wikipedia.org/wiki/Module_(mathematics)

https://encyclopediaofmath.org/wiki/Module

https://faculty.math.illinois.edu/~r-ash/Algebra/Chapter4.pdf

vt ka
- moodul (1)
- moodul (2)
- Z-moodul

# moodul (3)

olemus
algebraline süsteem, mis koosneb vektoritest ja skalaaridest
= a generalization of a vector space

Wiktionary:
6. (algebra, ring theory) an abelian group equipped with the operation of multiplication by an element of a ring (or another of certain algebraic objects), representing a generalisation of the concept of vector space with scalar multiplication

- vektoreid saab selles liita ja skalaariga korrutada
- liitmise suhtes on Abeli rühm
- skalaaride a, b ja vektorite x, y vahel kehtivad seosed:
a(bx) = (ab)x
1x = x
(a + b)x = ax + bx
a(x + y) = ax + ay

näide
iga aditiivne Abeli rühm, kui skalaarideks on täisarvude hulk

ülevaateid
https://mathworld.wolfram.com/Module.html

https://en.wikipedia.org/wiki/Module_(mathematics)

https://encyclopediaofmath.org/wiki/Module

https://faculty.math.illinois.edu/~r-ash/Algebra/Chapter4.pdf

vt ka
- moodul (1)
- moodul (2)
- Z-moodul

Palun oodake...

# moodul (3)

olemus
algebraline süsteem, mis koosneb vektoritest ja skalaaridest
= a generalization of a vector space

Wiktionary:
6. (algebra, ring theory) an abelian group equipped with the operation of multiplication by an element of a ring (or another of certain algebraic objects), representing a generalisation of the concept of vector space with scalar multiplication

- vektoreid saab selles liita ja skalaariga korrutada
- liitmise suhtes on Abeli rühm
- skalaaride a, b ja vektorite x, y vahel kehtivad seosed:
a(bx) = (ab)x
1x = x
(a + b)x = ax + bx
a(x + y) = ax + ay

näide
iga aditiivne Abeli rühm, kui skalaarideks on täisarvude hulk

ülevaateid
https://mathworld.wolfram.com/Module.html

https://en.wikipedia.org/wiki/Module_(mathematics)

https://encyclopediaofmath.org/wiki/Module