different between tensor vs vector

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

From Latin vector (“carrier, transporter”), from veh? (“I carry, I transport, I bear”).

The “person or entity that passes along an urban legend or other meme” sense derives from the disease sense.

The mathematics sense was coined by William Rowan Hamilton in 1846.

Pronunciation

• Hyphenation: vec?tor
• (UK) IPA^(key): /?v?kt?/
• (US) enPR: v?k't?r, IPA^(key): /?v?kt?/
• Rhymes: -?kt?(?)

Noun

vector (plural vectors)

1. (mathematics) A directed quantity, one with both magnitude and direction; the signed difference between two points.

   Hypernym: tensor
2. (mathematics) An ordered tuple representing a directed quantity or the signed difference between two points.
3. (mathematics) Any member of a (generalized) vector space.

4. (aviation) A chosen course or direction for motion, as of an aircraft.
6. (epidemiology) A carrier of a disease-causing agent.
7. (by extension, sociology) A person or entity that passes along an urban legend or other meme.
8. (psychology) A recurring psychosocial issue that stimulates growth and development in the personality.
9. The way in which the eyes are drawn across the visual text. The trail that a book cover can encourage the eyes to follow from certain objects to others.(Can we add an example for this sense?)
10. (computing, operating systems) A memory address containing the address of a code entry point, usually one which is part of a table and often one that is dereferenced and jumped to during the execution of an interrupt.
11. (programming) A one-dimensional array.
    • 2004, Jesse Liberty, Bradley L. Jones, Sams Teach Yourself C++ in 21 Days (page 694)

      To create a vector of students in a class, you will want the vector to be large enough […]

12. (computer graphics, attributive) A graphical representation using outlines; vector graphics.

    Coordinate term: raster

13. (molecular biology) A DNA molecule used to carry genetic information from one organism into another.

Usage notes

• (programming): The term vector is used loosely when the indices are not (either positive or non-negative) integers.

Hyponyms

Derived terms

Translations

Verb

vector (third-person singular simple present vectors, present participle vectoring, simple past and past participle vectored)

1. To set (particularly an aircraft) on a course toward a selected point.
2. (computing) To redirect to a vector, or code entry point.

Translations

References

• The New Oxford Dictionary of English

Anagrams

• Covert, corvet, covert

Catalan

Noun

vector m (plural vectors)

1. vector

Dutch

Etymology

Borrowed from Latin vector.

Pronunciation

• IPA^(key): /?v?k.t?r/
• Hyphenation: vec?tor
• Rhymes: -?kt?r

Noun

vector m (plural vectoren, diminutive vectortje n)

1. (mathematics) vector, an element of a vector space

Derived terms

• eenheidsvector
• eigenvector
• normaalvector
• nulvector
• raakvector
• vectoralgebra
• vectoranalyse
• vectordifferentiatie
• vectorlimiet
• vectorproduct
• vectorruimte
• vectorvermenigvuldiging

Galician

Etymology

From Latin vector

Noun

vector m (plural vectores)

1. vector

Derived terms

• vectorial
• vectorizar
• vectorización
• vector propio
• vector unitario

Latin

Etymology

veh? +? -tor

Pronunciation

• (Classical) IPA^(key): /?u?ek.tor/, [?u??kt??r]
• (Ecclesiastical) IPA^(key): /?vek.tor/, [?v?kt??r]

Noun

vector m (genitive vect?ris); third declension

1. bearer, carrier
2. passenger

Declension

Third-declension noun.

Related terms

• vect?gal

Descendants

• ? English: vector

Verb

vector

1. first-person singular present passive indicative of vect?

References

• vector in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
• vector in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
• Carl Meissner; Henry William Auden (1894) Latin Phrase-Book?^[2], London: Macmillan and Co.

Portuguese

Noun

vector m (plural vectores)

1. Superseded spelling of vetor.

Romanian

Etymology

From French vecteur.

Noun

vector m (plural vectori)

1. vector

Declension

Spanish

Etymology

From Latin vector.

Noun

vector m (plural vectores)

1. vector

Derived terms

• autovector
• eigenvector
• vectorial
• vectorizar
• vectorización
• vector propio
• vector unitario