Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I understand that the following is a linear combination of vectors $y_{1},..., y_{n}$:

$a_{1}y_{1} + a_{2}y_{2} + ... + a_{n}y_{n}$

My doubt is whether, the following which has an additional constant term $a_{0}$, can also be called a linear combination of vectors $y_{1},..., y_{n}$:

$a_{0} + a_{1}y_{1} + a_{2}y_{2} + ... + a_{n}y_{n}$

share|improve this question
4  
I assume your $a_i$s are scalars and your $y_j$s are vectors. What does it even mean to add a scalar to a vector? –  Chris Eagle Aug 23 '11 at 10:20

1 Answer 1

up vote 6 down vote accepted

No, it isn't. In fact, it doesn't make any sense, since $1$ -appearing in the first term as $a_0\cdot 1$, is not supposed to be a vector of your vector space, in general.

For instance, assume your vector space is $\mathbb{R}^2$: can you add $1$ to $(5,-3)$?

share|improve this answer
    
For some reason when combined with the OP's nickname and acceptance of the answer, I remembered my psychology while I was writing my thesis. :) –  user13838 Aug 23 '11 at 13:28

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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