Tensor

English

Etymology

Borrowed from Template:Bor, equivalent to Template:Af. Anatomical sense from 1704. Introduced in the 1840s by Template:Coin as an algebraic quantity unrelated to the modern notion of tensor. The contemporary mathematical meaning was introduced (as Template:Bor) 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, Template:Pedia)

Pronunciation

• Template:IPA
• Template:Audio
• Template:IPA
• Template:Rhymes

Noun

1. Template:Lb A muscle that tightens or stretches a part, or renders it tense. Template:Defdate

   Template:Hypo

2. Template:Lb A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array. Template:Defdate

   Template:Hyper

   Template:Hypo

   • Template:Quote-book
   1. Template:Lb A multidimensional array with (at least) two dimensions.
3. Template:Lb A norm operation on the quaternion algebra.

Usage notes

• The array's dimensionality (number of indices needed to label a component) is called its Template:M (also Template:M or Template:M).
  • In engineering usage the term is commonly used only for ranks of 2 (or more), contrasted with scalar and vectors.
• Tensors operate in the context of a vector space and thus within a choice of Template:W, 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 Template:W 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 Template:M is a pair of natural numbers (n, m), where n is the number of Template:M and m the number of Template:M. The total order of the tensor is the sum n + m.

Translations

• Bulgarian: Template:T
• Chinese:

  Mandarin: Template:T

• Finnish: Template:T
• Italian: Template:T+
• Polish: Template:T
• Tagalog: Template:T

• Czech: Template:T
• Esperanto: Template:T
• Finnish: Template:T+
• German: Template:T+
• Hindi: Template:T
• Icelandic: Template:T+
• Italian: Template:T+
• Norwegian: Template:T
• Polish: Template:T+
• Romanian: Template:T+
• Serbo-Croatian: Template:T+
• Swedish: Template:T+
• Tagalog: Template:T, Template:T
• Turkish: Template:T

• Arabic: Template:T
• Finnish: Template:T+
• French: Template:T+
• German: Template:T+
• Italian: Template:T+
• Norwegian: Template:T
• Polish: Template:T+
• Serbo-Croatian: Template:T+
• Swedish: Template:T+
• Tagalog: Template:T, Template:T
• Turkish: Template:T

• Arabic: Template:T
• Bulgarian: Template:T
• Finnish: Template:T+
• German: Template:T+
• Greek: Template:T
• Italian: Template:T+
• Norwegian: Template:T
• Polish: Template:T+
• Serbo-Croatian: Template:T+
• Swedish: Template:T+
• Tagalog: Template:T, Template:T
• Turkish: Template:T

Verb

1. To compute the tensor product of two tensors or algebraic structures.

References

• Template:R:Lexico
• Template:R:MWO

Anagrams

• Template:Anagrams

Dutch

Etymology

Ultimately or directly from Template:Der.

Pronunciation

• Template:IPA
• Template:Audio
• Template:Hyphenation
• Template:Rhyme

Noun

1. Template:Lb Template:L

Derived terms

• Template:L

Latin

Etymology

From Template:Af.

Pronunciation

• Template:La-IPA

Noun

1. that which stretches

Descendants

• Template:Desc

Polish

Noun

1. Template:Lb Template:L

Further reading

• Template:R:pl:PWN

Portuguese

Etymology

Template:Bor+.

Pronunciation

• Template:Rhymes
• Template:Hyph

Adjective

1. tensing; tensile

Noun

1. Template:Lb Template:L

Romanian

Etymology

Template:Bor+ or Template:Bor.

Noun

1. Template:Lb Template:L

Spanish

Adjective

1. tensing; tensile

Noun

1. Template:L

Further reading

• Template:R:es:DRAE

Swedish

Noun

1. Template:Lb Template:L; a function which is linear in all variables

Anagrams

• Template:Anagrams