Order of Graham-Schmidt Process

by rdfloyd
Tags: grahamschmidt, order, process
 P: 29 We learned the GSP yesterday in class, but my teacher said something that seems to conflict with the textbook. He said that we can set our first vector ($w_{1}$) equal to any vector in the set. However, I keep getting different answers than our textboook when I do this. My question: Is it possible to set the starting vector equal to any vector in the set? Then, do I have to continue the GSP in the order of the vector subscripts? For instance, assume that I have vectors $v_{1}, v_{2}$, and $v_{3}$. I want to set $v_{3}$ as my first vector $w_{1}$. So then my list becomes $v_{3}, v_{2}$, and $v_{1}$. Do I now have to do the order backwards, or can I do the order $v_{3}, v_{1}$ (going 1$\rightarrow$ 2 $\rightarrow$ 3), and $v_{2}$, etc.