Practice question · Match the pairs
Match each definiteness type to its geometric shape.
- Positive definite
- Negative definite
- Indefinite
- Positive semidefinite
- Dome (curves down in all directions)
- Saddle (up in some, down in others)
- Bowl (curves up in all directions)
- Trough (flat in one direction, up in others)
Hints
- Each classification corresponds to a shape.
- Opposite curvatures in different directions give a saddle.
Show the answer
- Positive definite → Bowl (curves up in all directions)
- Negative definite → Dome (curves down in all directions)
- Indefinite → Saddle (up in some, down in others)
- Positive semidefinite → Trough (flat in one direction, up in others)
Why
Definiteness determines curvature geometry, bowls, domes, saddles, and the flat borderline cases.
Practise Quadratic Forms
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