Gram Schmidt Orthogonalization

Question 1

If the vectors are not orthogonal, the we can convert this to a set of orthogonal vectors by an algorithm called _____.

Answer 1

Gram Schmidt Orthogonalization

Question 2

u1 = v1
u2 = v2 - 

uk = ____.

Answer 2

uk = Vk - projctn of Vk on u1 - prjctn of vk on u2 - …… - projctn of Vk on uk-1

Question 3

when does gram schmidt algo fail ___.

Answer 3

when vectors are not linearly independent

Question 4

projection is done from ___ dimension to ____dimension

Answer 4

higher to lower

Question 5

so many vectors to projcet on to the subspace then use ____

Answer 5

Gram schmidt to produce ortho basis and then use projection formula

Question 6

LS solution of Ax=b?

Answer 6

ATAx = ATb A matrix,b vector

Question 7

Compute LSS - 1st

Answer 7

AtA Atb

Question 8

2nd LSS

Answer 8

augumented matrix for matrix eqn and rwo red

Question 9

3d LSS

Answer 9

eqn consistent and any sol of x cap is a least square solution

Question 10

find least square solution menas the system is ____

Answer 10

inconsistent
b cannot be wriiten as linar comb of col of A
b cannot be find in col(A)

Question 11

if system is inconsistent and we need still to project

Answer 11

take closest vector by LSS

Question 12

how much unit away is Ax from b

Answer 12

norm (Ax - b)

after LSS