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Counterexample

Is this true?

Every real symmetric matrix is positive definite if det > 0

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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86 counterexamples are free — including most of the ones Part C leans on hardest.

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Invariants don't determine

Two objects sharing an invariant were treated as the same object.

See real exam options built on this mistakeDrill statements like this
linear algebraquadratic forms

Go deeper· Explained in full in Quadratic forms, signature and definiteness· Asked in CSIR NET June 2025· From Inner Product Spaces and Forms › Quadratic forms, positive definiteness, Sylvester's law

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