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
Famous quotes containing the word form:
“The place became full of a watchful intentness now; for when other things sank brooding to sleep the heath appeared slowly to awake and listen. Every night its Titanic form seemed to await something; but it had waited thus, unmoved, during so many centuries, through the crises of so many things, that it could only be imagined to await one last crisis—the final overthrow.”
—Thomas Hardy (1840–1928)