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The lines of a pencil joining the points of a line segment range to another point.

A quadratic form Q(x) is said to be positive semidefinite if it is never <0. However, unlike a positive definite quadratic form, there may exist a x!=0 such that the form is ...

The branch of formal logic, also called functional calculus, that deals with representing the logical connections between statements as well as the statements themselves.

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

The projective general orthogonal group PGO_n(q) is the group obtained from the general orthogonal group GO_n(q) on factoring the scalar matrices contained in that group.

The projective general unitary group PGU_n(q) is the group obtained from the general unitary group GU_n(q) on factoring the scalar matrices contained in that group.

A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime." An axiom is a proposition that is assumed to be true. With ...

An algebraic structure whose elements consist of selected homeomorphisms between open subsets of a space, with the composition of two transformations defined on the largest ...

A distance g on a set that fulfils the same properties as a metric except relaxes the definition to allow the distance between two different points to be zero. An example of ...

A field F in which any Pythagorean extension of F coincides with F.