Search Results for ""

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+....

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...

An invertible linear transformation T:V->W is a map between vector spaces V and W with an inverse map which is also a linear transformation. When T is given by matrix ...