Linear Algebra and Its Applications · Problem 6.2.5

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

If AA and BB are positive definite, then A+BA + B is positive definite. Pivots and eigenvalues are not convenient for A+BA + B. Much better to prove xT(A+B)x>0x^T(A+B)x > 0.

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