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What (who) is linear combination - definition

Linear combination

EXPRESSION CONSTRUCTED FROM A SET OF TERMS BY THE ADDITION OF TERMS IN THE SET TO EACH OTHER ANY NUMBER OF TIMES

Linear Algebra/Linear Combination; Linear combinations; Linear Combination; Linear algebra/Linear combination; Infinite linear combination

In mathematics, 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.

https://en.wikipedia.org/wiki/Linear_combination

Linear combination of atomic orbitals

TECHNIQUE IN QUANTUM CHEMISTRY

LCAO MO Method; Linear Combination of Atomic Orbitals Molecular Orbital Method; LCAO; LCAO-MO; Linear combinations of atomic orbitals; Linear Combination Of Atomic Orbitals; Linear combination of atomic orbitals molecular orbital method

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

https://en.wikipedia.org/wiki/Linear_combination_of_atomic_orbitals

linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

<mathematics> (Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v). (1996-09-30)