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.

Let $w = \mbox{span} \{(1,1,-2,0)^T,(1,0,2,1)^T\}$

Find an orthonormal basis for $w$ using dot product

share|improve this question
What have you tried? –  wj32 Oct 25 '12 at 1:19
I'm a bit confused as to what I actually need to do. Do I use gram-schmidt? I only have 2 vectors, don't I need 4 to solve this? if so, whats an easy way to choose 2 more vectors that I know are lineraly independant? –  straykiwi Oct 25 '12 at 1:25
$w$ is 2-dimensional, so you do not need 4 vectors. Have you read this article? en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process –  wj32 Oct 25 '12 at 1:26
Yeah I know how to use gram schmidt. w is 2 dimensional, but the vectors are 4 dimensional, does that matter? –  straykiwi Oct 25 '12 at 1:29
so v1 = (1,1,-2,0)trans and v2 = (1/2)*(3,1,2,2) Is what I got, is that correct? (next step would be to normalise v1 and v2?) –  straykiwi Oct 25 '12 at 1:31

1 Answer 1

up vote 0 down vote accepted

Just use Gram-Schmidt on $w$ which gives $$v_1 = \frac{1}{\sqrt{6}}(1,1,-2,0)$$ and $$v_2 = \frac{1}{3\sqrt{2}}(3,1,2,2).$$

share|improve this answer

Your Answer


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.