Subspace spanned by a vector


by cahiersujet
Tags: span subspace
cahiersujet
cahiersujet is offline
#1
Feb27-09, 12:09 PM
P: 5
What would the subspace spanned by a single vector (for example) f(x)=x+1 be?
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yyat
yyat is offline
#2
Feb27-09, 12:29 PM
P: 322
The subspace spanned by a vector is the set of all scalar multiples of that vector. A function like f(x)=x+1 is a "vector" in some function space, most likely over the real or complex numbers, so the answer is all functions of the form g(x)=a*(x+1), where a is an element of the scalar field (R or C).


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