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Definition of Linear operator
1. Noun. An operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions).
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: wiktionary.com
Lexicographical Neighbors of Linear Operator
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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