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A linear functional on a real vector space V is a function T:V->R, which satisfies the following properties. 1. T(v+w)=T(v)+T(w), and 2. T(alphav)=alphaT(v). When V is a ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

A sum of the elements from some set with constant coefficients placed in front of each. For example, a linear combination of the vectors x, y, and z is given by ax+by+cz, ...

A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When codewords are chosen ...

A linear extension of a partially ordered set P is a permutation of the elements p_1, p_2, ... of P such that p_i<p_j implies i<j. For example, the linear extensions of the ...

The kernel of a linear transformation T:V-->W between vector spaces is its null space.

A linear approximation to a function f(x) at a point x_0 can be computed by taking the first term in the Taylor series f(x_0+Deltax)=f(x_0)+f^'(x_0)Deltax+....

A root-finding algorithm also called Bailey's method and Hutton's method. For a function of the form g(x)=x^d-r, Lambert's method gives an iteration function ...

The conjugate gradient method is not suitable for nonsymmetric systems because the residual vectors cannot be made orthogonal with short recurrences, as proved in Voevodin ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...