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...
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A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum...
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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 + ⋯ +...
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be linearly independent if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists...
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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...
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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...
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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...
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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...
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Vector space (redirect from Linear space)
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...
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In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points...
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In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory...
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Quantum superposition (redirect from Quantum linear superposition)
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...
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identity mapping. A linear differential operator (abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential...
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Formal sum (redirect from Formal linear combination)
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...
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Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a...
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Symmetry-adapted linear combination may refer to: The linear combination of atomic orbitals in the subject of molecular orbitals Configuration state function...
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Nonlinear system (redirect from Non-linear)
linear combination of the unknown variables or functions that appear in them. Systems can be defined as nonlinear, regardless of whether known linear...
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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...
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by that type. This method of quantifying orbital contribution as a linear combination of atomic orbitals is used in computational chemistry. An additional...
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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...
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{\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 (...
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Artificial neuron (redirect from Linear neuron)
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...
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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...
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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...
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mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial....
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previous points and derivative values. In the case of linear multistep methods, a linear combination of the previous points and derivative values is used...
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Regression analysis (section Linear regression)
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...
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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...
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Least squares (section Linear least squares)
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...
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Gauss–Markov theorem (redirect from Best linear unbiased estimator)
\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 k j y k {\displaystyle...
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