explain how to determine 2 orthonormal basis using the vectors and .

Question

explain how to determine 2 orthonormal basis using the vectors <3,1> and <2,3>.

zarkon · Answer

the two vactors are linearly  independent so pick your two favorite orthonormal vectors

amistre64 · Answer

hmm, while that is accurate; I was looking more for a set of vectors that uses one and then the other in the basis itself :)

amistre64 · Answer

or at least the unit versions of them

anonymous · Answer

Are you interested in learning the Gram-Schmidt process?

amistre64 · Answer

already know the gram-schmidt; but was hoping for a more rudimentary explanation or justification for it ....

amistre64 · Answer

pictures and hand puppets kind thing lol

amistre64 · Answer

imran was having issues with it the other night which got me thinking how to explain it in a fundamental way.  v1 - (projv1 on v2) gives use an othogonal vector to v1

zarkon · Answer

|dw:1335548060851:dw|

zarkon · Answer

|dw:1335548142740:dw|

zarkon · Answer

|dw:1335548178688:dw|

zarkon · Answer

boy ...I'm not good at this  :)

amistre64 · Answer

lol, good enough tho :)  thats the basic concept underlying the algorithm ...

zarkon · Answer

that is the procedure I usually go through to derive the formula

zarkon · Answer

easier to do on the chalk board in the classroom. ;)

amistre64 · Answer

|dw:1335548262156:dw|

and the other set would amount to the other projection.

i was wondering if its taboo to use one over the other?

zarkon · Answer

no...that's fine...whatever gets the message across