In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding...

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum...

be linearly independent if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists...

K} , and multiplying a linear combination of S by a scalar c ∈ K {\displaystyle c\in K} will produce another linear combination of S: c ( λ 1 v 1 + ⋯ +...

to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used...

equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions...

written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates...

property of being closed under linear combinations. That is, a nonempty set W is a subspace if and only if every linear combination of finitely many elements...

are linearly independent if a linear combination results in the zero vector if and only if all its coefficients are zero. Linear subspace A linear subspace...

2: the first two columns are linearly independent, so the rank is at least 2, but since the third is a linear combination of the first two (the first column...

In statistics, linear regression is a model that estimates the linear relationship between a scalar response (dependent variable) and one or more explanatory...

In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points...

linear combination of the unknown variables or functions that appear in them. Systems can be defined as nonlinear, regardless of whether known linear...

identity mapping. A linear differential operator (abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential...

Symmetry-adapted linear combination may refer to: The linear combination of atomic orbitals in the subject of molecular orbitals Configuration state function...

In mathematics, a formal sum, formal series, or formal linear combination may be: In group theory, an element of a free abelian group, a sum of finitely...

by that type. This method of quantifying orbital contribution as a linear combination of atomic orbitals is used in computational chemistry. An additional...

In mathematics, an affine combination of x1, ..., xn is a linear combination ∑ i = 1 n α i ⋅ x i = α 1 x 1 + α 2 x 2 + ⋯ + α n x n , {\displaystyle \sum...

but they may also take the form of other nonlinear functions, piecewise linear functions, or step functions. They are also often monotonically increasing...

Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a...

completely non-relativistic. The variational solution is assumed to be a linear combination of a finite number of basis functions, which are usually (but not...

In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. Such classifiers...

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example...

mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial....

its partial derivatives. A regression model is a linear one when the model comprises a linear combination of the parameters, i.e., f ( x , β ) = ∑ j = 1...

previous points and derivative values. In the case of linear multistep methods, a linear combination of the previous points and derivative values is used...

product of outgoing particle states and a linear combination of ingoing particle states. The linear combination is given by a matrix known as the S-matrix...

coefficients of the linear combination of those basis polynomials that give the spline on that interval c0, ..., ck–2 Add up that linear combination of basis polynomial...

{\displaystyle \mathbf {y} (t)} are two valid solutions, then so is any linear combination of the two solutions, e.g., z ( t )   = d e f   α x ( t ) + β y (...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...