The bookUnit 1 · Inner Product Spaces and Forms28 / 83

Quadratic forms, positive definiteness, Sylvester's law

Why this is asked: Signature is the complete invariant over ℝ (Sylvester). Positive definiteness is tested by leading principal minors, or by all eigenvalues being positive — do not mix the two tests up.

Quadratic forms, signature and definiteness

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Testing definiteness, and reading Sylvester's lawinteractive

The leading-minors test done right — including the sign pattern for negative definite that catches people out.

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Open this in the full syllabus view · Unit 1