Gram-Schmidt Process

BigBoss22 · #1 $Old$ November 4th, 2009, 01:44 PM

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

tonio · #2 $Old$ November 4th, 2009, 09:47 PM

Quote:

Originally Posted by BigBoss22 $View Post$

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 $u,v\,,\,\,with\,\,\Arrowvert u \Arrowvert^2=<u,u>=1$ , then $v-<u,v>u$ is an orthogonal vector to $u$ , as can easily be checked (here, $<u,v>$ denotes the inner product of the vectors)

Tonio

BigBoss22 · #3 $Old$ November 5th, 2009, 12:42 AM

Thanks bro, didn't see how it got to 4, but now i understand