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\begin{bmatrix} a & b/2 \\ b/2 & c \end{bmatrix} {{attachment:coef.svg}}
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\begin{bmatrix} x & y \end{bmatrix} \begin{bmatrix} a & b/2 \\ b/2 & c \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} {{attachment:poly.svg}}

Quadratic Form

A quadratic form is a second-degree polynomial expressed as a linear combination of terms.


Description

The coefficients of a polynomial like ax2 + bxy + cy2 can also be expressed by matrix:

coef.svg

There are infinitely many solutions to x1,2 + x2,1 = b but by convention only x1,2 = b/2 is considered, as this gives a symmetric matrix.

It follows that a polynomial can be expressed as:

poly.svg


CategoryRicottone

LinearAlgebra/QuadraticForm (last edited 2026-08-12 21:57:39 by DominicRicottone)