Mathematics · University
Hessian determinant of a quadratic · formula reference
A positive determinant alone does not distinguish a local minimum from a maximum; inspect fₓₓ as well.
Formula
A positive determinant alone does not distinguish a local minimum from a maximum; inspect fₓₓ as well.
det H = fₓₓ fᵧᵧ − fₓᵧ²
Worked example
For f(x,y) = 11x² + (-7)xy + 11y², calculate the determinant of its Hessian. Round the final result to 4 decimal places if needed.
H = [[22,-7],[-7,22]]. Take the product of its diagonal entries minus the product of its off-diagonal entries.
435
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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