| 1. | This article considers mainly linear operators, which are the most common type.
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| 2. | Some operators ( specifically, self-adjoint linear operators ) correspond to physical observables.
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| 3. | Consider linear operators on a finite-dimensional vector space over a perfect field.
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| 4. | Orthogonal projection onto a line,, is a linear operator on the plane.
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| 5. | One may study this linear operator in the context of functional analysis.
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| 6. | Let and be Banach spaces and be a continuous linear operator.
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| 7. | Any linear operator defined on a finite-dimensional normed space is bounded.
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| 8. | Suppose that is a collection of continuous linear operators from to.
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| 9. | For example, a Fourier, Laplace transforms, and linear operator theory, that are applicable.
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| 10. | Linear operators also play a great role in the infinite-dimensional case.
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