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Vector Space of n-Tuples

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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)

see also:

  automatically generated 1/18/2005