Contraction (Tensor)
The contraction of a Tensor is obtained by setting unlike indices equal and summing according to theEinstein Summation convention. Contraction reduces the Rank of a Tensor by 2. For a second Rank Tensor,
Therefore, the contraction is invariant, and must be a Scalar. In fact, this Scalar is known as the Trace of a Matrix in Matrix theory.
References
Arfken, G. ``Contraction, Direct Product.'' §3.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 124-126, 1985.
- Helly Number
- Helly's Theorem
- Helmholtz Differential Equation
- Helmholtz Differential Equation--Bipolar Coordinates
- Helmholtz Differential Equation--Cartesian Coordinates
- Helmholtz Differential Equation--Circular Cylindrical Coordinates
- Helmholtz Differential Equation--Confocal Ellipsoidal Coordinates
- Helmholtz Differential Equation--Confocal Paraboloidal Coordinates
- Helmholtz Differential Equation--Conical Coordinates
- Helmholtz Differential Equation--Elliptic Cylindrical Coordinates
- Helmholtz Differential Equation--Oblate Spheroidal Coordinates
- Helmholtz Differential Equation--Parabolic Coordinates
- Helmholtz Differential Equation--Parabolic Cylindrical Coordinates
- Helmholtz Differential Equation Polar Coordinates
- Helmholtz Differential Equation--Prolate Spheroidal Coordinates
- Helmholtz Differential Equation--Spherical Coordinates
- Helmholtz Differential Equation--Spherical Surface
- Helmholtz Differential Equation--Toroidal Coordinates
- Helmholtz's Theorem
- Helson-Szegö Measure
- Hemicylindrical Function
- Hemisphere
- Hemispherical Function
- Hempel's Paradox
- Hendecagon