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Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

A symbol used to represent the point and space groups (e.g., 2/m3^_). Some symbols have abbreviated form. The equivalence between Hermann-Mauguin symbols (a.k.a. ...

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

The letter O is used for a number of different purposes in mathematics. The double-struck O is sometimes used to represent octonions. The symbols O(x) (sometimes called the ...

The letter O is used for a number of different purposes in mathematics. The double-struck O is sometimes used to represent octonions. The symbols O(x) (sometimes called the ...

"Aut" is the term applied in propositional calculus to the XOR connective. "Aut" is Latin form for "either/or (but not both)," e.g., "Aut Caesar aut nihil" (Cesare Borgia; ...

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

A dihedron is a regular tiling or map on a sphere composed of two regular p-gons, each occupying a hemisphere and with edge lengths of 2pi/p on a unit sphere. Its Schläfli ...