a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination...

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

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 + ⋯ +...

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

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...

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...

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...

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...

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

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...

In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory...

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...

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...

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

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

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

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...

{\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, 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...

linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function...

Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables...

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

sigmoid shape, but they may also take the form of other non-linear functions, piecewise linear functions, or step functions. They are also often monotonically...

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

common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data...

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...

general Bienaymé's identity. These results lead to the variance of a linear combination as: Var ⁡ ( ∑ i = 1 N a i X i ) = ∑ i , j = 1 N a i a j Cov ⁡ ( X...

is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables. In regression analysis, logistic...