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2. Tensor - Wikipedia

   en.wikipedia.org/wiki/Tensor

   The tensors are classified according to their type (n, m), where n is the number of contravariant indices, m is the number of covariant indices, and n + m gives the total order of the tensor. For example, a bilinear form is the same thing as a (0, 2)-tensor; an inner product is an example of a (0, 2)-tensor, but not all (0, 2)-tensors are inner ...

3. Category:Tensors - Wikipedia

   en.wikipedia.org/wiki/Category:Tensors

   In mathematics, a tensor is a certain kind of geometrical entity and array concept. It generalizes the concepts of scalar, vector and linear operator, in a way that is independent of any chosen frame of reference. For example, doing rotations over axis does not affect at all the properties of tensors, if a transformation law is followed.

4. Abstract index notation - Wikipedia

   en.wikipedia.org/wiki/Abstract_index_notation

   Abstract index notation (also referred to as slot-naming index notation) [1] is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis. [2] The indices are mere placeholders, not related to any basis and, in particular, are non-numerical.

5. Sage Manifolds - Wikipedia

   en.wikipedia.org/wiki/Sage_Manifolds

   New example worksheets. More classes and methods (some inherited from Sage). 0.4 10 February 2014 New classes, members, and methods. 0.5 12 July 2014 This is a major release, involving the introduction of algebraic structures to describe tensor fields, namely modules over the algebra of scalar fields, among which free modules of finite rank.

6. Glossary of tensor theory - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_tensor_theory

   The earliest foundation of tensor theory – tensor index notation. [1] Order of a tensor The components of a tensor with respect to a basis is an indexed array. The order of a tensor is the number of indices needed. Some texts may refer to the tensor order using the term degree or rank. Rank of a tensor The rank of a tensor is the minimum ...

7. Cartesian tensor - Wikipedia

   en.wikipedia.org/wiki/Cartesian_tensor

   A dyadic tensor T is an order-2 tensor formed by the tensor product ⊗ of two Cartesian vectors a and b, written T = a ⊗ b.Analogous to vectors, it can be written as a linear combination of the tensor basis e x ⊗ e x ≡ e xx, e x ⊗ e y ≡ e xy, ..., e z ⊗ e z ≡ e zz (the right-hand side of each identity is only an abbreviation, nothing more):