Glossary of tensor theory
This is a glossary of tensor theory. For expositions of tensor theory from different points of view, see:
For some history of the abstract theory see also multilinear algebra.
Classical notation
;Ricci calculus;Order of a tensor
;Rank of a tensor
;Dyadic tensor
;Einstein notation
;Kronecker delta
;Levi-Civita symbol
;Covariant tensor
;Contravariant tensor
;Mixed tensor
;Cartesian tensor
;Contraction of a tensor
;Raising and lowering indices
;Symmetric tensor
;Antisymmetric tensor
;Multiple cross products
Algebraic notation
This avoids the initial use of components, and is distinguished by the explicit use of the tensor product symbol.;Tensor product
;Pure tensor
;Tensor algebra
;Hodge star operator
;Exterior power
;Symmetric power, symmetric algebra
Applications
;Metric tensor;Strain tensor
;Stress–energy tensor
Tensor field theory
;Jacobian matrix;Tensor field
;Tensor density
;Lie derivative
;Tensor derivative
;Differential geometry
Abstract algebra
;Tensor product of fields;Tensor product of R-algebras
;Clifford module
;Tor functors
;Symbolic method of invariant theory
;Derived category
;Grothendieck's six operations
Spinors
See:;Spin group
;Spin-c group
;Spinor
;Pin group
;Pinors
;Spinor field
;Killing spinor
;Spin manifold