Linear Algebra and Its Applications · Problem 6.3.7

Positive Definite Matrices — Gilbert Strang

Mathematics · singular-value-decomposition

Problem

Construct the matrix with rank 1 that has

Av = 12u

for

v = \frac{1}{2}(1,1,1,1)

and

u = \frac{1}{3}(2,2,1)

. Its only singular value is

\sigma_1 = \underline{\quad}