Linear Algebra and Its Applications · Problem 3.4.29

Orthogonality — Gilbert Strang

Mathematics · gram-schmidt-orthogonal-vectors

Problem

(Recommended) Find orthogonal vectors

A

B

C

by Gram-Schmidt from

a

b

c

a = (1, -1, 0, 0) \qquad b = (0, 1, -1, 0) \qquad c = (0, 0, 1, -1).

A

B

C

and

a

b

c

are bases for the vectors perpendicular to

d = (1, 1, 1, 1)