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...

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

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...

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...

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

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

generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes...

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...

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...

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...

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...

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

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...

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...

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...

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

\varepsilon _{j})=0,\forall i\neq j.} A linear estimator of β j {\displaystyle \beta _{j}} is a linear combination β ^ j = c 1 j y 1 + ⋯ + c n j y n {\displaystyle...

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 (...

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

convex conical hull of S is a closed set. Affine combination Convex combination Linear combination Convex Analysis and Minimization Algorithms by Jean-Baptiste...

In algebraic topology, a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes)...

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 linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

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

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

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...

The superposition principle means that a linear combination of inputs to the system produces a linear combination of the individual zero-state outputs (that...

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