0
$\begingroup$

span{s+v} = span{s} + span{v}

Does the above statement always hold true?

In addition, what is the difference between span {s} $\cup$ {v} = span{s} + span{v} and the above statement?

$\endgroup$
  • 1
    $\begingroup$ Are $s$ and $v$ vectors or sets of vectors? If they are sets, how are you defining $s+v$? If they are vectors, how are you defining $s\cup v$? $\endgroup$ – EuYu Mar 24 '13 at 9:09
  • $\begingroup$ Do you mean span {$s$}$\cup${$u$}=Span{$s$}+span{$v$}? $\endgroup$ – jim Mar 24 '13 at 9:12
  • $\begingroup$ Hey i edited the question. Hope it is clear now. $\endgroup$ – uohzxela Mar 24 '13 at 9:17
4
$\begingroup$

No. Consider the set {$(1,0)+(0,1)$} $=$ {$(1,1)$}.

The span of {$(1,1)$} is just a straight line through the origin in $\mathbb{R}^{2}.$ While the span of {$(0,1)$,$(1,0)$} is all of $\mathbb{R}^{2}$.

On the other hand span({$s$} $\cup$ {$v$}) $=$ span{$s$} + span{$v$} holds.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.