Tensorとは 意味・読み方・使い方

語源

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 )

発音

• (Received Pronunciation) IPA: /ˈtɛn.sə/, /ˈtɛn.sɔː/
• (General American) IPA: /ˈtɛn.sɚ/, /ˈtɛn.sɔɹ/
• 韻: -ɛnsə(ɹ)

名詞

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

   • 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.

   1. (engineering, computing) A multidimensional array with (at least) two dimensions.

      Coordinate terms: scalar, vector

3. (mathematics, obsolete) A norm operation on the quaternion algebra.

使用する際の注意点

(mathematics, linear algebra):

• The array's dimensionality (number of indices needed to label a component) is called its order (also degree or rank).
  • 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 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.

派生語

動詞

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 or algebraic structures.

参照

• “tensor”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.
• “tensor”, in Merriam-Webster Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.

アナグラム

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

発音

• (Classical Latin) IPA: [ˈtẽː.sɔr]
• (modern Italianate Ecclesiastical) IPA: [ˈt̪ɛn.sor]

名詞

tēnsor m (genitive tēnsōris); third declension (New Latin)

1. that which stretches

Inflection

Third-declension noun.

派生した語

• → English: tensor