Linear Algebra and Its Applications · Problem 3.4.19

Orthogonality — Gilbert Strang

Mathematics · modified-gram-schmidt

Problem

Show that these modified Gram-Schmidt steps produce the same

C

as in equation (10):

C^* = c - (q_1^T c) q_1 \quad \text{and} \quad C = C^* - (q_2^T C^*) q_2.

This is much more stable, to subtract the projections one at a time.