Linear Algebra and Its Applications · Problem 3.4.3

Orthogonality — Gilbert Strang

Mathematics · projection-orthonormal-basis

Problem

Find also the projection of

b = (0, 3, 0)

onto

a_3 = (\frac{2}{3}, -\frac{1}{3}, \frac{2}{3})

, and add the three projections. Why is

P = a_1 a_1^T + a_2 a_2^T + a_3 a_3^T

equal to

I