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 occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric), differential topology (intersection forms of four-manifolds), and Lie theory (the Killing form).
Read more about Quadratic Form: Introduction, History, Real Quadratic Forms, Definitions, Equivalence of Forms, Geometric Meaning, Integral Quadratic Forms
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“It is absolutely impossible to transcend the laws of nature. What can change in historically different circumstances is only the form in which these laws expose themselves.”
—Karl Marx (1818–1883)