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Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

For any Abelian group G and any natural number n, there is a unique space (up to homotopy type) such that all homotopy groups except for the nth are trivial (including the ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; |; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a ...

A zonotope is a set of points in d-dimensional space constructed from vectors v_i by taking the sum of a_iv_i, where each a_i is a scalar between 0 and 1. Different choices ...

States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment ...

The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from pi:G->G/H. Namely, the open ...

The normal bundle of a submanifold N in M is the vector bundle over N that consists of all pairs (x,v), where x is in N and v is a vector in the vector quotient space ...

A bounded linear operator T in B(H) on a Hilbert space H is said to be cyclic if there exists some vector v in H for which the set of orbits ...