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Linear differential equation

DIFFERENTIAL EQUATIONS THAT ARE LINEAR WITH RESPECT TO THE UNKNOWN FUNCTION AND ITS DERIVATIVES

Constant coefficients; Linear differential equations; General solution; Linear ordinary differential equation; First-order nonhomogeneous linear differential equation; First order linear differential equation; Linear ODE; Linear homogeneous differential equation; First-order linear differential equation; System of linear differential equations; Solution of a differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

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

Differential-linear attack

FORM OF CRYPTANALYSIS

Differential-linear cryptanalysis

Introduced by Martin Hellman and Susan K. Langford in 1994, the differential-linear attack is a mix of both linear cryptanalysis and differential cryptanalysis.

https://en.wikipedia.org/wiki/Differential-linear_attack

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)