Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online course: Linear Algebra - Basic Structures - Vector Spaces

Vector Space of n-Tuples


[previous page] [next page] [table of contents][page overview]

Let $ K$ be a field. Then the $ n$-tuple,

$\displaystyle a = (a_1,\ldots,a_n)^{\operatorname t},\quad a_i\in K\, ,
$

endowed with addition and multiplication by components, form the $ K$-vector space $ K^n$, where addition and multiplication by components mean:

$\displaystyle (a_1,\ldots,a_n)^{\operatorname t}+ (b_1,\ldots,b_n)^{\operatorname t}=
(a_1+b_1,\ldots,a_n+b_n)^{\operatorname t}
$

and

$\displaystyle \lambda (a_1,\ldots,a_n)^{\operatorname t}=
(\lambda a_1,\ldots,\lambda a_n)^{\operatorname t}
$

for $ a_i,b_i,\lambda\in K$.
(Authors: App/Burkhardt/Höllig)

  automatically generated 4/21/2005