In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,
is a quadratic form in the variables x and y.
Quadratic forms are central objects in mathematics, occurring for instance in number theory, geometry (Riemannian metric), topology (intersection forms on homology), and Lie theory (the Killing form). They are also ubiquitous in physics and chemistry, as the energy of a system, particularly in relation to the L2 norm, which leads to the use of Hilbert spaces.
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