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A real normed algebra, also called a composition algebra, is a multiplication * on R^n that respects the length of vectors, i.e., |x*y|=|x|*|y| for x,y in R^n. The only real ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a modular Hilbert algebra if A has an inner product <··> and a ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

A Kähler metric is a Riemannian metric g on a complex manifold which gives M a Kähler structure, i.e., it is a Kähler manifold with a Kähler form. However, the term "Kähler ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

The order of the polynomial defining an algebraic curve.

A point at which two noncrossing branches of a curve meet with different tangents.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, ...