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WordNet-Online
Definitions from WordNet | ||||
Definitions from the WebLinear OperatorA linear operator refers to a mathematical function that operates on vectors, transforming them in a way that preserves certain structural properties. It is commonly used in linear algebra and functional analysis. Sense 1: MathematicsIn mathematics, a linear operator is a function that maps one vector space to another, while preserving the vector addition and scalar multiplication operations. It can be represented by a matrix and is often used to describe transformations in geometric spaces. Example sentence:"The linear operator multiplied the vector by a constant and rotated it in the plane." Sense 2: Computer ScienceIn computer science, a linear operator refers to an algorithm or function that applies a linear transformation to a set of data points or a matrix. It is utilized in various computational tasks such as image processing, data compression, and machine learning. Example sentence:"The linear operator efficiently reduced the dimensionality of the dataset, improving the computational performance." Sense 3: PhysicsIn physics, a linear operator represents an operation or transformation that obeys the principles of linearity, meaning it satisfies the superposition principle. It is used to model various physical phenomena, including quantum mechanics and wave equations. Example sentence:"The wave function evolves according to the linear operator defined by Schrödinger's equation." Possible Related Products on Amazon: | ||||
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