tensorn.

Brit.

/ˈtɛnsə/, U.S.

/ˈtɛnsər/,

/ˈtɛnˌsɔr/

Etymology: < modern Latin tensor, agent-noun < tendĕre to stretch.

1. Anatomy. Also tensor muscle. A muscle that stretches or tightens some part. Opposed to laxator.In modern use, distinguished from an extensor by not altering the direction of the part.

ΘΚΠ

the world > life > the body > structural parts > muscle > types of muscles > [noun]

sphincter1578

raiser1588

in-muscle?1609

oblique1612

abducens1615

abductor1615

adductor1615

antagonist1615

bender1615

depressor1615

extender1615

flexor1615

levator1615

quadratus1615

rectus1615

retractor1615

sphincter-muscle1615

accelerator1638

bicepsa1641

elevator1646

adducent1649

lifter1649

rotator1657

flector1666

contractor1682

dilater1683

orbicularis palpebrarum1694

transverse muscle1696

tensor muscle1704

biventer1706

extensor1713

attollent1728

constrictor1741

dilator1741

risibles1785

orbicularis oculi1797

obliquus1799

erector1828

extensor-muscle1830

compressor1836

trans-muscle1836

antagonizer1844

motor1846

evertor1848

inflector1851

protractor1853

prime mover1860

orbicular1872

transversalis1872

invertor1875

skeletal muscle1877

dilatator1878

occlusor muscle1878

sphincter1879

pilomotor1892

agonist1896

1704 J. Harris Lexicon Technicum I Tensors, or Extensors, are those common Muscles that serve to extend the Toes, and have their Tendons inserted into all the lesser Toes.

1799 Home in Philos. Trans. (Royal Soc.) 90 10 The combined action of the tensor and laxator muscles varying the degree of its [the membrana tympani] tension.

1808 J. Barclay Muscular Motions 384 The biceps..being a flexor and supinator of the fore-arm, and at the same time a tensor of its fascia.

1879 St. George's Hosp. Rep. 9 591 The functions of the adductors and tensors are more delicate.

2. Mathematics.

a. In Quaternions, a quantity expressing the ratio in which the length of a vector is increased.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > quaternion > factor or operator in

tensor1846

versora1865

1846 W. R. Hamilton in London, Edinb. & Dublin Philos. Mag. 3rd Ser. 29 27 Since the square of a scalar is always positive, while the square of a vector is always negative, the algebraical excess of the former over the latter square is always a positive number; if then we make (TQ)² = (SQ)² − (VQ)², and if we suppose TQ to be always a real and positive or absolute number, which we may call the tensor of the quaternion Q, we shall not thereby diminish the generality of that quaternion. This tensor is what was called in former articles the modulus.

1853 W. R. Hamilton Elem. Quaternions (1866) ii. i. 108 The former element of the complex relation..between..two lines or vectors [viz. their relative length], is..represented by a simple ratio.., or by a number expressing that ratio. Note, This number, which we shall..call the tensor of the quotient,..may always be equated..to a positive scalar.

1886 W. S. Aldis Elem. Solid Geom. (ed. 4) xiv. 235 Since the operation denoted by a quarternion consists of two parts, one of rotating OA into the position OB and the other of extending OA into the length OB, a quaternion may be..represented as the product of two factors,..the versor..and..the tensor of the quaternion.

b. An abstract entity represented by an array of components that are functions of co-ordinates such that, under a transformation of co-ordinates, the new components are related to the transformation and to the original components in a definite way. [This sense is due to W. Voigt ( Die Fund. Physik. Eigenschaften der Krystalle (1898) p. vi).]

ΘΚΠ

the world > matter > physics > relativity > [noun] > tensor

tensor1916

Weyl tensor1962

the world > relative properties > number > mathematical number or quantity > tensor > [noun]

Riemann–Christoffel tensor1916

tensor1916

Riemann tensor1922

Ricci tensor1923

Riemann curvature tensor1923

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > array > other

magic square1704

Pascal's triangle1886

tensor1916

payoff matrix1950

payoff table1960

1916 Monthly Notices Royal Astron. Soc. 76 701 In the four-dimensional time-space we consider tensors of different orders. The tensor of order zero is a pure number (scalar), the tensor of the first order is a vector, which has 4 components, the tensor of the second order has 16 components, and so on.

1916 Monthly Notices Royal Astron. Soc. 76 702 If once we have expressed the laws of nature in the form of linear relations between tensors, they will be invariant for all transformations. Thus with the aid of the calculus of tensors Einstein has succeeded in satisfying the postulate of general relativity.

1934 Nature 20 Oct. 612 The theory of tensors, so important in physics and geometry on account of their property of vanishing in every co-ordinate system if they vanish in one, was created by Ricci (1887) and his pupil Levi-Civita, although the name tensor was not introduced by them.

1943 Jrnl. London Math. Soc. 18 109 The study of the particular class of invariants known as tensors goes back to the work of Riemann and Christoffel on quadratic differential forms.

1953 C.-T. Wang Applied Elasticity i. 1 Stress is called a tensor, because in addition to its magnitude, direction, and sense, which define a vector, it depends on another vector, which represents the surface upon which it acts.

1970 G. K. Woodgate Elem. Atomic Struct. iii. 50 The operator in eqn. (3.95) is a component of a second-rank tensor, the atomic electric quadrupole moment.

1974 G. Reece tr. F. Hund Hist. Quantum Theory xv. 211 ψ and χ were scalars, spinors, vectors or tensors.

Compounds

C1. General attributive.

tensor algebra n.

ΚΠ

1922Tensor algebra [see tensor analysis n.].

1936 Electr. Engin. (U.S.) 55 1214/1 The object of this paper is to apply tensor algebra to the solution of the circuits of multi-winding transformers.

1971 C. W. Curtis in M. B. Powell & G. Higman Finite Simple Groups iii. 142 Form a vector space M with basis X, and let ℱ_x be the tensor algebra over M.

tensor analysis n.

ΚΠ

1922 H. H. L. A. Brose tr. Weyl Space–Time–Matter i. 58 Tensor analysis tells us how, by differentiating with respect to the space co-ordinates, a new tensor can be derived from the old one in a manner entirely independent of the co-ordinate system. This method, like tensor algebra, is of extreme simplicity.

1939 G. Kron Tensor Anal. Networks p. xvi Tensor analysis may be considered as an extension and generalization of vector analysis from three- to n-dimensional spaces and from Euclidean to non-Euclidean spaces.

1976 Sci. Amer. Aug. 98/2 Einstein's ideas were cast in a language very different from even non-Euclidean geometry, called the absolute differential calculus... Einstein used it and changed its name to tensor analysis.

1977 D. Bagley Enemy xxxiii. 266 This joker is using Hamiltonian quaternions!.. No one..has used Hamiltonian quaternions since 1915 when tensor analysis was invented.

tensor calculus n.

ΚΠ

1922 H. H. L. A. Brose tr. Weyl Space–Time–Matter i. 53 The study of tensor-calculus is, without doubt, attended by conceptual difficulties—over and above the apprehension inspired by indices.

1944 G. B. Shaw Everybody's Polit. What's What? ii. 22 Experts in the tensor calculus.

1981 Sci. Amer. July 95/1 Tensor calculus..was essential to Einstein's formulation of his general theory of relativity.

tensor product n.

ΚΠ

1964 A. P. Robertson & W. Robertson Topol. Vector Spaces vii. 141 It is essential to form the completion of the tensor product under the correct topology.

1965 G. Birkhoff & S. MacLane Surv. Mod. Algebra (ed. 3) vii. 188 Show that tensor products are distributive on direct sums.

1971 E. C. Dade in M. P. Powell & G. Higman Finite Simple Groups viii. 252 The tensor product..is again a finite-dimensional vector space over F.

C2.

tensor field n. a field for which a tensor is defined at each point.

ΘΚΠ

the world > matter > physics > relativity > [noun] > tensor > field defining

tensor field1922

1922 H. H. L. A. Brose tr. Weyl Space–Time–Matter i. 61 An important example of a tensor field is offered by the stresses occurring in an elastic body.

1934 R. C. Tolman Relativity, Thermodynamics, & Cosmol. 36 Tensor fields may..be constructed, in which a value of the field tensor is associated with each point in the continuum.

tensor force n. a force between two bodies that has to be expressed as a tensor rather than a vector, esp. a non-central force between subatomic particles.

ΘΚΠ

the world > matter > physics > relativity > [noun] > tensor > force expressed as

tensor force1947

1947 Physical Rev. 72 987/1 The result of the present calculation and that of the proton–neutron scattering, which includes the tensor forces, show that the difference among the three potentials is quite pronounced at these high energies.

1972 Physics Bull. June 349/2 The noncentral force causing the anomalies mentioned above is called the tensor force, and it results from a neutron–protonspin–spin interaction.

tensor-twist n. in Clifford's biquaternions, a twist multiplied by a tensor.

Derivatives

tenˈsorial adj.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > tensor > [adjective]

tensorial1934

1934 Chem. Abstr. 28 5327 (title) Tensorial fields accompanying the Dirac electron: neutrino and antineutrino.

1968 C. G. Kuper Introd. Theory Superconductivity iv. 58 Since..Pippard's experimental data..do not support the idea of a tensorial anisotropy, these equations have not proved useful.

This entry has not yet been fully updated (first published 1911; most recently modified version published online March 2022).

单词	tensor
释义	tensorn. Brit. /ˈtɛnsə/, U.S. /ˈtɛnsər/, /ˈtɛnˌsɔr/ Etymology: < modern Latin tensor, agent-noun < tendĕre to stretch. 1. Anatomy. Also tensor muscle. A muscle that stretches or tightens some part. Opposed to laxator.In modern use, distinguished from an extensor by not altering the direction of the part. ΘΚΠ the world > life > the body > structural parts > muscle > types of muscles > [noun] sphincter1578 raiser1588 in-muscle?1609 oblique1612 abducens1615 abductor1615 adductor1615 antagonist1615 bender1615 depressor1615 extender1615 flexor1615 levator1615 quadratus1615 rectus1615 retractor1615 sphincter-muscle1615 accelerator1638 bicepsa1641 elevator1646 adducent1649 lifter1649 rotator1657 flector1666 contractor1682 dilater1683 orbicularis palpebrarum1694 transverse muscle1696 tensor muscle1704 biventer1706 extensor1713 attollent1728 constrictor1741 dilator1741 risibles1785 orbicularis oculi1797 obliquus1799 erector1828 extensor-muscle1830 compressor1836 trans-muscle1836 antagonizer1844 motor1846 evertor1848 inflector1851 protractor1853 prime mover1860 orbicular1872 transversalis1872 invertor1875 skeletal muscle1877 dilatator1878 occlusor muscle1878 sphincter1879 pilomotor1892 agonist1896 1704 J. Harris Lexicon Technicum I Tensors, or Extensors, are those common Muscles that serve to extend the Toes, and have their Tendons inserted into all the lesser Toes. 1799 Home in Philos. Trans. (Royal Soc.) 90 10 The combined action of the tensor and laxator muscles varying the degree of its [the membrana tympani] tension. 1808 J. Barclay Muscular Motions 384 The biceps..being a flexor and supinator of the fore-arm, and at the same time a tensor of its fascia. 1879 St. George's Hosp. Rep. 9 591 The functions of the adductors and tensors are more delicate. 2. Mathematics. a. In Quaternions, a quantity expressing the ratio in which the length of a vector is increased. ΘΚΠ the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > quaternion > factor or operator in tensor1846 versora1865 1846 W. R. Hamilton in London, Edinb. & Dublin Philos. Mag. 3rd Ser. 29 27 Since the square of a scalar is always positive, while the square of a vector is always negative, the algebraical excess of the former over the latter square is always a positive number; if then we make (TQ)² = (SQ)² − (VQ)², and if we suppose TQ to be always a real and positive or absolute number, which we may call the tensor of the quaternion Q, we shall not thereby diminish the generality of that quaternion. This tensor is what was called in former articles the modulus. 1853 W. R. Hamilton Elem. Quaternions (1866) ii. i. 108 The former element of the complex relation..between..two lines or vectors [viz. their relative length], is..represented by a simple ratio.., or by a number expressing that ratio. Note, This number, which we shall..call the tensor of the quotient,..may always be equated..to a positive scalar. 1886 W. S. Aldis Elem. Solid Geom. (ed. 4) xiv. 235 Since the operation denoted by a quarternion consists of two parts, one of rotating OA into the position OB and the other of extending OA into the length OB, a quaternion may be..represented as the product of two factors,..the versor..and..the tensor of the quaternion. b. An abstract entity represented by an array of components that are functions of co-ordinates such that, under a transformation of co-ordinates, the new components are related to the transformation and to the original components in a definite way. [This sense is due to W. Voigt ( Die Fund. Physik. Eigenschaften der Krystalle (1898) p. vi).] ΘΚΠ the world > matter > physics > relativity > [noun] > tensor tensor1916 Weyl tensor1962 the world > relative properties > number > mathematical number or quantity > tensor > [noun] Riemann–Christoffel tensor1916 tensor1916 Riemann tensor1922 Ricci tensor1923 Riemann curvature tensor1923 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > array > other magic square1704 Pascal's triangle1886 tensor1916 payoff matrix1950 payoff table1960 1916 Monthly Notices Royal Astron. Soc. 76 701 In the four-dimensional time-space we consider tensors of different orders. The tensor of order zero is a pure number (scalar), the tensor of the first order is a vector, which has 4 components, the tensor of the second order has 16 components, and so on. 1916 Monthly Notices Royal Astron. Soc. 76 702 If once we have expressed the laws of nature in the form of linear relations between tensors, they will be invariant for all transformations. Thus with the aid of the calculus of tensors Einstein has succeeded in satisfying the postulate of general relativity. 1934 Nature 20 Oct. 612 The theory of tensors, so important in physics and geometry on account of their property of vanishing in every co-ordinate system if they vanish in one, was created by Ricci (1887) and his pupil Levi-Civita, although the name tensor was not introduced by them. 1943 Jrnl. London Math. Soc. 18 109 The study of the particular class of invariants known as tensors goes back to the work of Riemann and Christoffel on quadratic differential forms. 1953 C.-T. Wang Applied Elasticity i. 1 Stress is called a tensor, because in addition to its magnitude, direction, and sense, which define a vector, it depends on another vector, which represents the surface upon which it acts. 1970 G. K. Woodgate Elem. Atomic Struct. iii. 50 The operator in eqn. (3.95) is a component of a second-rank tensor, the atomic electric quadrupole moment. 1974 G. Reece tr. F. Hund Hist. Quantum Theory xv. 211 ψ and χ were scalars, spinors, vectors or tensors. Compounds C1. General attributive. tensor algebra n. ΚΠ 1922Tensor algebra [see tensor analysis n.]. 1936 Electr. Engin. (U.S.) 55 1214/1 The object of this paper is to apply tensor algebra to the solution of the circuits of multi-winding transformers. 1971 C. W. Curtis in M. B. Powell & G. Higman Finite Simple Groups iii. 142 Form a vector space M with basis X, and let ℱ_x be the tensor algebra over M. tensor analysis n. ΚΠ 1922 H. H. L. A. Brose tr. Weyl Space–Time–Matter i. 58 Tensor analysis tells us how, by differentiating with respect to the space co-ordinates, a new tensor can be derived from the old one in a manner entirely independent of the co-ordinate system. This method, like tensor algebra, is of extreme simplicity. 1939 G. Kron Tensor Anal. Networks p. xvi Tensor analysis may be considered as an extension and generalization of vector analysis from three- to n-dimensional spaces and from Euclidean to non-Euclidean spaces. 1976 Sci. Amer. Aug. 98/2 Einstein's ideas were cast in a language very different from even non-Euclidean geometry, called the absolute differential calculus... Einstein used it and changed its name to tensor analysis. 1977 D. Bagley Enemy xxxiii. 266 This joker is using Hamiltonian quaternions!.. No one..has used Hamiltonian quaternions since 1915 when tensor analysis was invented. tensor calculus n. ΚΠ 1922 H. H. L. A. Brose tr. Weyl Space–Time–Matter i. 53 The study of tensor-calculus is, without doubt, attended by conceptual difficulties—over and above the apprehension inspired by indices. 1944 G. B. Shaw Everybody's Polit. What's What? ii. 22 Experts in the tensor calculus. 1981 Sci. Amer. July 95/1 Tensor calculus..was essential to Einstein's formulation of his general theory of relativity. tensor product n. ΚΠ 1964 A. P. Robertson & W. Robertson Topol. Vector Spaces vii. 141 It is essential to form the completion of the tensor product under the correct topology. 1965 G. Birkhoff & S. MacLane Surv. Mod. Algebra (ed. 3) vii. 188 Show that tensor products are distributive on direct sums. 1971 E. C. Dade in M. P. Powell & G. Higman Finite Simple Groups viii. 252 The tensor product..is again a finite-dimensional vector space over F. C2. tensor field n. a field for which a tensor is defined at each point. ΘΚΠ the world > matter > physics > relativity > [noun] > tensor > field defining tensor field1922 1922 H. H. L. A. Brose tr. Weyl Space–Time–Matter i. 61 An important example of a tensor field is offered by the stresses occurring in an elastic body. 1934 R. C. Tolman Relativity, Thermodynamics, & Cosmol. 36 Tensor fields may..be constructed, in which a value of the field tensor is associated with each point in the continuum. tensor force n. a force between two bodies that has to be expressed as a tensor rather than a vector, esp. a non-central force between subatomic particles. ΘΚΠ the world > matter > physics > relativity > [noun] > tensor > force expressed as tensor force1947 1947 Physical Rev. 72 987/1 The result of the present calculation and that of the proton–neutron scattering, which includes the tensor forces, show that the difference among the three potentials is quite pronounced at these high energies. 1972 Physics Bull. June 349/2 The noncentral force causing the anomalies mentioned above is called the tensor force, and it results from a neutron–protonspin–spin interaction. tensor-twist n. in Clifford's biquaternions, a twist multiplied by a tensor. Derivatives tenˈsorial adj. ΘΚΠ the world > relative properties > number > mathematical number or quantity > tensor > [adjective] tensorial1934 1934 Chem. Abstr. 28 5327 (title) Tensorial fields accompanying the Dirac electron: neutrino and antineutrino. 1968 C. G. Kuper Introd. Theory Superconductivity iv. 58 Since..Pippard's experimental data..do not support the idea of a tensorial anisotropy, these equations have not proved useful. This entry has not yet been fully updated (first published 1911; most recently modified version published online March 2022). > see also also refers to : tensertensorn. < n.1704 see also
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tensorn.

Compounds

Derivatives

> see also