Linear Algebra and Its Applications · Problem 6.3.6

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition

Problem

Suppose

u_1,\ldots,u_n

and

v_1,\ldots,v_n

are orthonormal bases for

\mathbf{R}^n

. Construct the matrix

A

that transforms each

v_j

into

u_j

to give

Av_1 = u_1,\ldots,Av_n = u_n