different between tensor vs expand

English

Etymology

Borrowed from New Latin tensor (“that which stretches”), equivalent to tense +? -or. Anatomical sense from 1704.Introduced in the 1840s 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) 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. (See, for example, Cauchy stress tensor on Wikipedia.Wikipedia )

Pronunciation

• (Received Pronunciation) IPA^(key): /?t?n.s?/, /?t?n.s??/
• (General American) IPA^(key): /?t?n.s?/, /?t?n.s??/
• Rhymes: -?ns?(?)

Noun

tensor (plural tensors or (muscle) tensores)

1. (anatomy) A muscle that tightens or stretches a part, or renders it tense. [from 17th c.]

   Hyponyms: tensor fasciae latae, tensor tympani, tensor veli palatini

2. (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array. [from 18th c.]

   Hypernym: function

   Hyponyms: duotensor, eigentensor, Faraday tensor, hypertensor, metric tensor, pseudotensor, subtensor, supertensor, vector, Weyl tensor, zero tensor

3. (mathematics, obsolete) 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.

Derived terms

Translations

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

• “tensor”, in Lexico, Dictionary.com; Oxford University Press, 2019–present.
• “tensor”, in Merriam–Webster Online Dictionary, (Please provide a date or year).

Anagrams

• -setron, Nestor, Nortes, Reston, Sterno, Stoner, Trones, noters, sterno-, stoner, tenors, toners, trones

Dutch

Etymology

Ultimately or directly from Latin tensor.

Pronunciation

• IPA^(key): /?t?n.z?r/, /?t?n.s?r/
• Hyphenation: ten?sor
• Rhymes: -?nz?r

Noun

tensor m (plural tensoren)

1. (mathematics, linear algebra) tensor

Derived terms

• tensoralgebra

Latin

Etymology

From tend? (“stretch, distend, extend”) +? -tor (agent suffix).

Pronunciation

• (Classical) IPA^(key): /?ten.sor/, [?t???s??r]
• (Ecclesiastical) IPA^(key): /?ten.sor/, [?t??ns?r]

Noun

tensor m (genitive tens?ris); third declension (New Latin)

1. that which stretches

Inflection

Third-declension noun.

Descendants

• ? English: tensor

Polish

Pronunciation

• IPA^(key): /?t??.s?r/

Noun

tensor m inan

1. (mathematics) tensor

Declension

Derived terms

• tensorowy

Spanish

Adjective

tensor (feminine tensora, masculine plural tensores, feminine plural tensoras)

1. tensing; tensile

Noun

tensor m (plural tensores)

1. tensor

Derived terms

Swedish

Noun

tensor c

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

Declension

Anagrams

• noters, ortens, rosten, rotens, sorten, toners

English

Etymology

Recorded in Middle English since 1422 (as expanden, expaunden), from Anglo-Norman espaundre, from Latin expandere present active infinitive of expand? (“to spread out”), itself from ex- (“out, outwards”) + pand? (“to spread”). Doublet of spawn.

Pronunciation

• Rhymes: -ænd
• IPA^(key): /?k?spænd/

Verb

expand (third-person singular simple present expands, present participle expanding, simple past and past participle expanded)

1. (transitive) To change (something) from a smaller form or size to a larger one; to spread out or lay open.

2. (transitive) To increase the extent, number, volume or scope of (something).
3. (transitive) To express (something) at length and/or in detail.
4. (transitive, algebra) To rewrite (an expression) as a longer, yet equivalent sum of terms.

5. (intransitive, algebra, of an expression) To become, by rewriting, a longer, yet equivalent sum of terms.

6. (transitive, arithmetic) To multiply both the numerator and the denominator of a fraction by the same natural number yielding a fraction of equal value
7. (intransitive) To change or grow from smaller to larger in form, number, or size.

8. (intransitive) To increase in extent, number, volume or scope.
9. (intransitive) To speak or write at length or in detail.
10. (intransitive) To feel generous or optimistic.

Synonyms

• (to change from a smaller form/size to a larger one): open out, spread, spread out, unfold
• (to increase the extent, number, volume or scope of): enlarge
• (to express at length or in detail): elaborate (on), expand on

Antonyms

• (to change from a smaller form/size to a larger one): contract
• (to increase the extent, number, volume or scope of): contract
• (algebra: to rewrite as an equivalent sum of terms): factor

Derived terms

• expandable
• expander

Related terms

• expanse
• expansible
• expansile
• expansive
• expansion
• expansionism

Translations