Linear Algebra and Its Applications · Problem 3.2.24

Orthogonality — Gilbert Strang

Mathematics · cosines-projections-onto-lines

Problem

Project the vector

b = (1,1)

onto the lines through

a_1 = (1,0)

and

a_2 = (1,2)

. Draw the projections

p_1

and

p_2

and add

p_1 + p_2

. The projections do not add to

b

because the

a

's are not orthogonal.