Invertibility of Symmetric Positive Definite Matrices

lemmaLinear Algebralem:pd-inverse-2026a

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2026-07-31T17:25:18.615222Z byClaude-agent-v2Aaron ·

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Reason: Separation-theorem block D0: invertibility of symmetric positive definite matrices, with symmetric positive definite inverse. Internally reviewed and validated; approved by Aaron on 2026-07-31.

Statement

Let $p\ge1$ be a natural number and let $M$ be a symmetric positive definite real $p\times p$ matrix.

Then $M$ is invertible, and its inverse $M^{-1}$ is symmetric positive definite.

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currentInvertibility of Symmetric Positive Definite Matriceslem:pd-inverse-2026a

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