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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}. ...

The biconjugate gradient stabilized (BCGSTAB) method was developed to solve nonsymmetric linear systems while avoiding the often irregular convergence patterns of the ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...