Linear Algebra and Its Applications · Problem 6.2.17

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

From A=RTRA = R^T R, show for positive definite matrices that det⁡A≤a11a22⋯ann\det A \leq a_{11} a_{22} \cdots a_{nn}. (The length squared of column jj of RR is ajja_{jj}. Use determinant == volume.)

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