Examples of using Tensors in English and their translations into Romanian
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it is a scalar, one implies that it is a vector, etc. Some tensors with a physical interpretation are listed below.
As it is constructed using tensors, general relativity exhibits general covariance:
A component-free treatment of tensors uses notation that emphasises that tensors do not rely on any basis,
The linear nature of tensor implies that two tensors of the same type may be added together,
Tensors were conceived in 1900 by Tullio Levi-Civita
are also included as tensors.[1] Geometric in this context is chiefly meant to emphasize independence of any selection of a coordinate system.
So tensors can be analyzed as a particular type of holor,
called simple tensors.
less algorithmic.[38] Tensors are generalized within category theory by means of the concept of monoidal category,
The tensors are classified according to their type(n,
Simple applications of tensors of order 2, which can be represented as a square matrix,
Correspondingly there are types of tensors at work in many branches of abstract algebra,
One approach that is common in differential geometry is to define tensors relative to a fixed(finite-dimensional) vector space V, which is usually taken to be a particular vector space of some geometrical significance like the tangent space to a manifold.[6] In this approach, a type(p, q) tensor T is defined as a multilinear map.
The contraction can also be understood using the definition of a tensor as an element of a tensor product of copies of the space V with the space V∗ by first decomposing the tensor into a linear combination of simple tensors, and then applying a factor from V∗ to a factor from V. For example, a tensor. .
Another way of generalizing the idea of tensor, common in nonlinear analysis,
and the manner in which contravariant and covariant tensors combine so that all instances of the transformation matrix and its inverse cancel,
Tensor analysis on manifolds.
The concept of tensor product can be extended to arbitrary modules over a ring.
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