List of mathematic operators
In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators.
In the following L is an operator
which takes a function to another function . Here, and are some unspecified function spaces, such as Hardy space, Lp space, Sobolev space, or, more vaguely, the space of holomorphic functions.
Expression | Curve definition |
Variables | Description |
---|---|---|---|
Linear transformations | |||
Derivative of nth order | |||
Cartesian |
| Integral, area | |
Composition operator | |||
Even component | |||
Odd component | |||
Difference operator | |||
Backward difference (Nabla operator) | |||
Indefinite sum operator (inverse operator of difference) | |||
Sturm–Liouville operator | |||
Non-linear transformations | |||
Inverse function | |||
Legendre transformation | |||
Left composition | |||
Indefinite product | |||
Logarithmic derivative | |||
Elasticity | |||
Schwarzian derivative | |||
Total variation | |||
Arithmetic mean | |||
Geometric mean | |||
Cartesian |
| Subtangent | |
Parametric Cartesian |
| ||
Polar |
| ||
Polar |
| Sector area | |
Cartesian |
| Arc length | |
Parametric Cartesian |
| ||
Polar |
| ||
Cartesian |
| Affine arc length | |
Parametric Cartesian |
| ||
Parametric Cartesian |
| ||
Cartesian |
| Curvature | |
Parametric Cartesian |
| ||
Polar |
| ||
Parametric Cartesian |
| ||
Cartesian |
| Affine curvature | |
Parametric Cartesian |
| ||
Parametric Cartesian |
| Torsion of curves | |
| Parametric Cartesian |
| Dual curve (tangent coordinates) |
| Parametric Cartesian |
| Parallel curve |
| Parametric Cartesian |
| Evolute |
Intrinsic |
| ||
| Parametric Cartesian |
| Involute |
| Parametric Cartesian |
| Pedal curve with pedal point (0;0) |
| Parametric Cartesian |
| Negative pedal curve with pedal point (0;0) |
| Intrinsic |
| Intrinsic to Cartesian transformation |
Metric functionals | |||
Norm | |||
Inner product | |||
Fubini–Study metric (inner angle) | |||
Distribution functionals | |||
Convolution | |||
Differential entropy | |||
Expected value | |||
Variance |
See also
This article is issued from
Wikipedia.
The text is licensed under Creative Commons - Attribution - Sharealike.
Additional terms may apply for the media files.