Linear Operator definition of Linear Operator in the Free Online Encyclopedia.

linear operator [′lin·ē·ər ′äp·ə‚rād·ər]

(mathematics)

Linear Operator

a generalization of the concept of linear transformation to vector spaces. F is called a linear operator on a vector space E if it is a function on E with values in some vector space E₁ and has the linearity property

F(αx + βy) = αF(x) + βF(y)

where x and y are elements of E, and α and β are numbers. If the E and E₁ are normed spaces and ǀǀF(x)ǀǀ / ǀǀxǀǀ is uniformly bounded for all x ∈ E, then the linear operator F is said to be bounded and

is called its norm.

The most important linear operators on function spaces are the differential linear operators

and the integral linear operators

The Laplace operator is an example of a linear operator on a space of functions of many variables. The theory of linear operators finds numerous applications in various problems of mathematical physics and applied mathematics.

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No references found	9781604564945 Non-Archimedean linear operators and applications. Non-Archimedean linear operators and applications by SciTech Book News Now a linear operator S with dense domain D(S) is called symmetric if <S[phi], [psi]> = <[phi], S[psi]) for all [psi], [phi] [member of] D(S). Approximation of bandlimited functions on a non-compact manifold by ... by Martin, R.; Kempf, A. / Sampling Theory in Signal and Image Processing The homotopy analysis method provides great freedom to choose proper initial approximations, auxiliary linear operator and auxiliary functions. Convergence of the homotopy decomposition method for solving ... by Xuehui, Chen; Liancun, Zheng; Xinxin, Zhang / Advances in Dynamical Systems and Applications	Linear Function of a Vector Linear Functional Linear Graph Notation linear hypothesis linear independence linear inequalities linear integrated circuit Linear Interpolation linear light linear light source linear logic linear magnetic amplifier Linear Magnification linear manifold linear map linear measure linear meter linear model linear modulation linear molecule linear momentum linear motion Linear Motor linear network Linear Network Synthesis Linear Operator linear order linear oscillator linear packer linear parallax linear parallel texture linear plan linear polarization linear polymer Linear Pottery Culture linear power amplifier linear prestressing Linear Programming linear rectifier linear regression linear regulator problem linear repeater linear scale linear scanning Linear Scripts Linear Space linear span linear speed method linear Stark effect linear stopping power linear strain	Linear motor Linear motor linear motors linear motors Linear Multi-Resolution Vector Quantizer Linear Multi-State Consecutively-Connected System Linear Multi-State Sliding-Window System Linear Multi-User Detection Linear Multistage Receiver Linear Multivariate Statistical Analysis Linear Nautical Mile Linear navigation Linear Near Certainty Error linear network Linear Network Autocorrelation Model Linear Network Synthesis Linear Nevus Sebaceous Syndrome Linear no threshold hypothesis Linear no-threshold model Linear No-threshold Theory Linear Noise Block Linear Nonlinear Learning Linear Normal Constant Tangential Basis Function Linear Normal Form Linear numbers Linear Opacity Judgment Linear Operator Linear operators Linear Optical Amplifier Linear Optical Sensors Linear Optics Quantum Computing Linear Optimal Control System Linear Optimal Distribution Linear optimization Linear optimization Linear optimization Linear Optimization Problem Linear order Linear ordering Linear ordinary differential equation Linear ordinary differential equation Linear Ordinary Differential Operator linear oscillator linear osteotomy linear osteotomy linear osteotomy Linear Output Saturated Counter linear packer Linear Packing Density Model Linear Pair Postulate linear parallax Linear Parallel Interference Cancellation linear parallel texture Linear Parameter Measurement Linear Parameter-Varying Linear partial differential equation Linear partial differential equation

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9781604564945 Non-Archimedean linear operators and applications.

Non-Archimedean linear operators and applications by SciTech Book News

Now a linear operator S with dense domain D(S) is called symmetric if <S[phi], [psi]> = <[phi], S[psi]) for all [psi], [phi] [member of] D(S).

Approximation of bandlimited functions on a non-compact manifold by ... by Martin, R.; Kempf, A. / Sampling Theory in Signal and Image Processing

The homotopy analysis method provides great freedom to choose proper initial approximations, auxiliary linear operator and auxiliary functions.

Convergence of the homotopy decomposition method for solving ... by Xuehui, Chen; Liancun, Zheng; Xinxin, Zhang / Advances in Dynamical Systems and Applications

Linear Function of a Vector