Linear Algebra and Its Applications · Problem 6.1.17

Positive Definite Matrices — Gilbert Strang

Mathematics · positive-definite-matrices-tests-for-positive-definiteness

Problem

(Important)(\textit{Important}) If AA has independent columns, then ATAA^T A is square and symmetric and invertible (Section 4.2). Rewrite xTATAxx^T A^T A x to show why it is positive except when x=0x = 0. Then ATAA^T A is positive definite.

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