Mathematics-Online course: Linear Algebra-Basic Structures-Vector Spaces-Vector Space of n-Tuples

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	Mathematics-Online course: Linear Algebra - Basic Structures - Vector Spaces
	Vector Space of n-Tuples

Let

be a field. Then the

-tuple,

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

endowed with addition and multiplication by components, form the

-vector space

, 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