A quadratic form is a homogeneous polynomial of degree two in multiple variables, represented typically as $$Q(x) = x^T A x$$, where $$x$$ is a vector of variables and $$A$$ is a symmetric matrix. Quadratic forms play an essential role in optimization problems and are used to analyze the curvature of functions. Understanding their properties helps in solving systems of equations and applying various numerical methods, particularly in iterative algorithms like the conjugate gradient method.
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