Definition of Linear operator

1. Noun. An operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions).

Generic synonyms: Operator

Definition of Linear operator

1. Noun. (mathematics functional analysis) An operator L such that for functions ''f'' and ''g'' and scalar ?, L (''f'' + ''g'') = L ''f'' + L ''g'' and L ?''f'' = ? L ''f''. ¹

¹ Source:

Lexicographical Neighbors of Linear Operator

linear combinations
linear dependence
linear dichroism
linear energy transfer
linear equation
linear equations
linear fracture
linear function
linear functional
linear functions
linear independence
linear leaf
linear measure
linear models
linear operator (current term)
linear operators
linear pair
linear pairs
linear perspective
linear programming
linear regression
linear skull fracture
linear system
linear transformation
linear transformations
linear unit

Literary usage of Linear operator

Below you will find example usage of this term as found in modern and/or classical literature:

1. Electromagnetic Theory by Oliver Heaviside (1893)
"The naturalness of the result is obvious, when the relativity of motion is remembered. The General linear operator. § 168. It is now necessary to leave ..."

2. Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups by John Edward Campbell (1903)
"The operator U being permutable with every linear operator, we have (U,X) = 0, (U,Y) = 0, (X,Y) = aX + bY+cU, where a, b, c are some constants. ..."

3. Stochastic Differential Equations in Infinite Dimensional Spaces by Gopinath Kallianpur, Jie Xiong (1995)
"T is called a linear operator from X to Y if T is a linear map defined on a subspace ... It is obvious that T' is a linear operator. Definition 1.2.2 Let X, ..."

4. Vectorial Mechanics by Ludwik Silberstein (1913)
"But if it happens that then a) is called a symmetrical linear operator, and the vector B = o,A is called a symmetrical linear function of A. The symmetrical ..."

5. Real Analysis by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)
"Definition 12.22 A linear operator T : X —> Y is bounded if there exists M > 0 such that ||Tx|| < Af||x|| for all xG X. The operator norm for a bounded ..."

6. Elements of Vector Algebra by Ludwik Silberstein (1919)
"We have already seen that the self-conjugate linear operator <o can be represented as a symmetrical dyadic. We may still mention that the general linear ..."

7. Optimality: The Second Erich L. Lehmann Symposium by Javier Rojo (2006)
"Let T denote a linear operator on a linear space H, a complex Hilbert space. If, to every g € G, there is assigned a linear operator T(g) such that, ..."

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