Im trying to understand the Gram-Schmidt process but i cant see how the part in this attatchment works?
Could you please describe what's going on here?
Thanks for any help in advance
What is inside that parentheses is then scalar product (inner product) of those two vectors, the result of which is 4 which then multiplies the rightmost matrix and then this is substracted from the first one.
In general, if you have two linearly independent vectors $\displaystyle u,v\,,\,\,with\,\,\Arrowvert u \Arrowvert^2=<u,u>=1$, then $\displaystyle v-<u,v>u$ is an orthogonal vector to $\displaystyle u$, as can easily be checked (here, $\displaystyle <u,v>$ denotes the inner product of the vectors)
Tonio