Let $\{e_1,e_2,\ldots,e_n\}$ be orthonormal basis of $V$ and let $v_1,v_2,\ldots,v_n$ are vectors in $V$. If $\|e_j-v_j\|<1/ \sqrt n$ for $j=1,2,\ldots,n$ then how can we prove that $\{v_1,v_2,\ldots,v_n\}$ is basis for $V$?
Asked
Active
Viewed 68 times
1
-
3See here: http://math.stackexchange.com/questions/1732753/proving-a-basis-for-inner-product-space-v-when-e-j-v-j-frac1-sqrtn – carmichael561 Nov 27 '16 at 00:10
-
2Or there : http://math.stackexchange.com/questions/2017821/show-linear-independence-of-a-set-of-vectors-close-to-an-orthonormal-basis?rq=1 – Arnaud D. Nov 27 '16 at 00:15
-
@ArnaudD. Thanks a lot – Jamal Gadirov Nov 27 '16 at 00:17