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A linear real-valued function omega^1 of vectors v such that omega^1(v)|->R. Vectors (i.e., contravariant vectors or "kets" |psi>) and one-forms (i.e., covariant vectors or ...

A pullback is a general categorical operation appearing in a number of mathematical contexts, sometimes going under a different name. If T:V->W is a linear transformation ...

The Rabinovich-Fabrikant equation is the set of coupled linear ordinary differential equations given by x^. = y(z-1+x^2)+gammax (1) y^. = x(3z+1-x^2)+gammay (2) z^. = ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...

Let K and L be simplicial complexes, and let f:K^((0))->L^((0)) be a map. Suppose that whenever the vertices v_0, ..., v_n of K span a simplex of K, the points f(v_0), ..., ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

If T is a linear transformation of R^n, then the null space Null(T), also called the kernel Ker(T), is the set of all vectors X such that T(X)=0, i.e., Null(T)={X:T(X)=0}. ...