Linear Algebra and Its Applications · Problem 6.2.6

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

From the pivots, eigenvalues, and eigenvectors of

A = \begin{bmatrix} 5 & 4 \\ 4 & 5 \end{bmatrix}

, write

A

R^T R

in three ways:

(L\sqrt{D})(\sqrt{D}L^T)

(Q\sqrt{\Lambda})(\sqrt{\Lambda}Q^T)

, and

(Q\sqrt{\Lambda}Q^T)(Q\sqrt{\Lambda}Q^T)