Linear Algebra and Its Applications · Problem 3.4.16

Orthogonality — Gilbert Strang

Mathematics · gram-schmidt-qr

Problem

Express the Gram-Schmidt orthogonalization of

a_1

a_2

A = QR

a_1 = \begin{bmatrix} 1 \\ 2 \\ 2 \end{bmatrix}, \quad a_2 = \begin{bmatrix} 1 \\ 3 \\ 1 \end{bmatrix}.

Given

n

vectors

a_i

with

m

components, what are the shapes of

A

Q

, and

R