# tensor

## English

### Etymology

From New Latin tensor (that which stretches). Anatomical sense from 1704. In the 1840s introduced by William Rowan Hamilton as an algebraic quantity unrelated to the modern notion of tensor. The contemporary mathematical meaning was introduced (as German Tensor) by Woldemar Voigt (1898)[1] and adopted in English from 1915 (in the context of General Relativity), obscuring the earlier Hamiltonian sense. The mathematical object is so named because an early application of tensors was the study of materials stretching under tension.

### Pronunciation

tensor (not comparable)

1. Of or relating to tensors.

### Noun

tensor (plural tensors)

1. (anatomy) A muscle that stretches a part, or renders it tense.
2. (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other tensors, and is represented as a multidimensional array.[2]
• 1963, Richard Feynman, “Chapter 31, Tensors”, in The Feynman Lectures on Physics, volume II:
The tensor ${\displaystyle \alpha _{ij}}$ should really be called a “tensor of second rank,” because it has two indexes. A vector—with one index—is a tensor of the first rank, and a scalar—with no index—is a tensor of zero rank.
3. () A norm operation on the quaternion algebra.

#### Usage notes

(mathematics, linear algebra):

• The array's dimensionality (number of indices needed to label a component) is called its order (also degree or rank).
• Tensors operate in the context of a vector space and thus within a choice of basis vectors, but, because they express relationships between vectors, must be independent of any given choice of basis. This independence takes the form of a law of covariant and/or contravariant transformation that relates the arrays computed in different bases. The precise form of the transformation law determines the type (or valence) of the tensor. The tensor type is a pair of natural numbers (n, m), where n is the number of contravariant indices and m the number of covariant indices. The total order of the tensor is the sum n + m.

### Verb

tensor (third-person singular simple present tensors, present participle tensoring, simple past and past participle tensored)

1. To compute the tensor product of two tensors.

### References

1. ^ W. Voigt, Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung, Leipzig, Germany: Veit & Co., 1898, p. 20.
2. ^ Rowland, Todd and Weisstein, Eric W., "Tensor", Wolfram MathWorld.

## Polish

Polish Wikipedia has an article on:
Wikipedia pl

tensor m inan

## Spanish

### Noun

tensor m (plural tensores)

## Swedish

### Noun

tensor c

1. (mathematics) tensor; a function which is linear in all variables

#### Declension

Declension of tensor
Singular Plural
Indefinite Definite Indefinite Definite
Nominative tensor tensorn tensorer tensorerna
Genitive tensors tensorns tensorers tensorernas