Quadratic forms

“distance” level sets {v : v^TA v = c} in R²

Symmetric matrix A

(

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A is kept symmetric: a₁₂ = a₂₁.

Presets

Classification

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Eigenvalues

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Chosen point

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The level sets {v : v^TA v = c} are the points at fixed “A-distance” √c from the origin.
c > 0 c < 0
principal axes (eigenvectors) chosen point v
Drag ● to move v and read off v^TA v.