invariantadj.n.

/ɪnˈvɛːrɪənt/

Etymology: < in- prefix⁴ + variant adj. and n.

A. adj.

a. Unvarying, invariable.

ΘΚΠ

the world > time > change > absence of change, changelessness > [adjective]

fasteOE

inunvariable1535

uniform1559

changeless1575

unvariant1582

wasteless1589

unchanging1595

inherent1601

unselfchanging1605

shiftless1606

ne'er-changinga1616

waxlessa1618

immutable1621

equal1626

irreducible1633

indiminishable1641

imprevaricable1644

Median1649

undiminishable1653

assiduous1661

unvarying1690

unfluctuating1723

unrelapsing1740

stable1742

unarbitrary1793

untransferable1794

unaltering1813

constant1817

all-or-nothing1853

all-or-none1864

reducelessc1864

unaugmentable1868

invariant1874

inadaptive1886

plateaued1899

steady state1909

hardcore1951

homoeostatic1955

monochromatic1959

1874 G. H. Lewes Probl. Life & Mind I. 95 Each cause is invariant; it is only the phenomena that are variable.

1957 G. E. Hutchinson Treat. Limnol. I. ix. 634 The relatively invariant climatic conditions of the equatorial regions.

1964 J. M. Argyle Psychol. & Social Probl. i. 14 These so-called ‘first-order factors’ are not a satisfactory final solution, since they will reflect the numbers of tests of different kinds which have been used, and fail to yield a stable or ‘invariant’ set of factors.

1966 [see sense B. 2].

1973 Sci. Amer. Feb. 26/1 The locations of nerve cells, the trajectories of nerve fibers and the spatial arrays of synaptic connections are invariant in all individuals of the same species. This invariance is termed neuronal specificity.

b. Physical Chemistry. Having no degrees of freedom (see freedom n. 12b).

ΘΚΠ

the world > matter > chemistry > physical chemistry > phases > [adjective] > degrees of freedom > no degrees

invariant1899

1899 R. A. Lehfeldt Text-bk. Physical Chem. v. 208 Such systems may conveniently be called invariant, univariant, divariant, &c., according as they possess no, one, two, &c., degrees of freedom.

1923 A. C. D. Rivett Phase Rule i. 25 When F = o the system is said to be invariant, since none of its variables may be altered at will without destroying the system in the sense of altering the number of coexisting phases.

1971 F. A. Bettelheim Exper. Physical Chem. xxvii. 259 Phase diagrams of ternary systems that are plotted on a triple co-ordinate graph have two important features: an invariant point, O, and the solubility curves.

c. Mathematics and Physics. Unchanged by a specified transformation or operation. Const. under.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > being invariant or covariant

invariantive1878

covariant1905

invariant1908

1908 H. Hilton Introd. Theory Groups Finite Order v. 62 If every element of a group G transforms an element g of G into itself, so that g is permutable with every element of G, g is called a normal, self-conjugate, or invariant element of G... Similarly, if every element of G transforms a subgroup H into itself, H is called a normal, self-conjugate, or invariant subgroup of G.

1914 L. Silberstein Theory of Relativity iv. 111 The principle of relativity excludes all such laws as are not invariant with respect to the Lorentz transformation.

1919 A. N. Whitehead Enq. Princ. Nat. Knowl. 39 They [sc. Newton's equations] are invariant for the spatio-temporal transformations from one such set to another within the Newtonian group.

1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra vi. 153 A subgroup S of a group G is normal (in G) if and only if it is invariant under all inner automorphisms of G (i.e., contains with any element all its conjugates).

1955 W. Pauli in W. Pauli Niels Bohr & Devel. Physics 34 The theory is invariant with respect to space or time reflection separately.

1968 Amer. Jrnl. Physics 36 1103/2 The two Einstein postulates state that the laws of physics and speed of light do not change for relatively moving reference systems (being covariant and invariant, respectively).

B. n. Mathematics.

a. A function of the coefficients of a quantic such that, if the quantic be linearly transformed, the same function of the new coefficients is equal to the first function multiplied by some power of the modulus of transformation. Also attributive.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > invariant

resultant1842

invariant1851

catalecticant1852

sextinvariant1852

reciprocant1886

1851 J. J. Sylvester in London, Edinb., & Dublin Philos. Mag. 4th Ser. 2 396 The remaining coefficients are the two well-known hyperdeterminants, or, as I propose henceforth to call them, the two Invariants of the form ax⁴ + 4bx³y + 6cx²y² + 4dxy³ + ey⁴.

1851 J. J. Sylvester in London, Edinb., & Dublin Philos. Mag. 4th Ser. 2 399 If I (a, b,..l) = I (a′, b′,..l′), then I is defined to be an invariant of f.

1873 H. Spencer Study Sociol. (1882) 223 I learn that the Theory of Invariants and the methods of investigation which have grown out of it constitute a step in mathematical progress larger than any made since the Differential Calculus.

1908 J. E. Wright Invariants of Quadratic Differential Forms Pref. The aim of this tract is to give..an account of the invariant theory connected with a single quadratic differential form.

1940 J. L. Coolidge Hist. Geom. Methods ii. ii. 156 The invariant idea, thus launched, was eagerly seized on, especially..by the great twin brethren, Cayley and Sylvester.

b. Any quantity or expression which is invariant under a specified transformation or operation.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > invariant under specific operation

invariant1908

1908 H. Hilton Introd. Theory Groups Finite Order vii. 99 An expression is an invariant of [a substitution-group] G if it is not altered when we perform on it every one of a set of substitutions which generate G.

1914 L. Silberstein Theory of Relativity iv. 112 It may be expressed shortly by saying that x² + y² + z² — c²t²..is a relativistic invariant.

1956 E. M. Patterson Topol. i. 11 Such entities are called topological invariants, because they are the same for all topologically equivalent spaces.

1959 Chambers's Encycl. I. 260/2 The extensive theory of invariants and covariants has many applications in geometry.

1967 E. U. Condon & H. Odishaw Handbk. Physics (ed. 2) i. x. 144/1 In theory of relativity the distinction between quantities which change with the reference system (covariants) and quantities which do not change with the reference system (invariants) is of paramount importance.

2. gen. An invariant property or feature.

ΘΚΠ

the world > time > change > absence of change, changelessness > [noun] > something unchanging

leopard1382

the law of the Medes and Persiansc1384

constant1832

hardcore1916

invariance1939

invariant1939

facticity1964

1939 Mind 48 39 There is a widespread view that the sole invariant of morals is their sociological function to secure the preservation and welfare of a social group.

1960 K. M. Delavenay & E. Delavenay Introd. Machine Transl. iii. 28 In 1949 Weaver pointed out that..one discovers statistical invariants, as found in cryptography.., semantic invariants,..and logical invariants.

1966 J. J. Katz Philos. Lang. ii. 9 The study of language in general provides us with generalizations expressing the invariant features of language which we may particularize as the requirement that an empirically correct description of a natural language represents such invariants.

This entry has not yet been fully updated (first published 1900; most recently modified version published online September 2018).

单词	invariant
释义	invariantadj.n. /ɪnˈvɛːrɪənt/ Etymology: < in- prefix⁴ + variant adj. and n. A. adj. a. Unvarying, invariable. ΘΚΠ the world > time > change > absence of change, changelessness > [adjective] fasteOE inunvariable1535 uniform1559 changeless1575 unvariant1582 wasteless1589 unchanging1595 inherent1601 unselfchanging1605 shiftless1606 ne'er-changinga1616 waxlessa1618 immutable1621 equal1626 irreducible1633 indiminishable1641 imprevaricable1644 Median1649 undiminishable1653 assiduous1661 unvarying1690 unfluctuating1723 unrelapsing1740 stable1742 unarbitrary1793 untransferable1794 unaltering1813 constant1817 all-or-nothing1853 all-or-none1864 reducelessc1864 unaugmentable1868 invariant1874 inadaptive1886 plateaued1899 steady state1909 hardcore1951 homoeostatic1955 monochromatic1959 1874 G. H. Lewes Probl. Life & Mind I. 95 Each cause is invariant; it is only the phenomena that are variable. 1957 G. E. Hutchinson Treat. Limnol. I. ix. 634 The relatively invariant climatic conditions of the equatorial regions. 1964 J. M. Argyle Psychol. & Social Probl. i. 14 These so-called ‘first-order factors’ are not a satisfactory final solution, since they will reflect the numbers of tests of different kinds which have been used, and fail to yield a stable or ‘invariant’ set of factors. 1966 [see sense B. 2]. 1973 Sci. Amer. Feb. 26/1 The locations of nerve cells, the trajectories of nerve fibers and the spatial arrays of synaptic connections are invariant in all individuals of the same species. This invariance is termed neuronal specificity. b. Physical Chemistry. Having no degrees of freedom (see freedom n. 12b). ΘΚΠ the world > matter > chemistry > physical chemistry > phases > [adjective] > degrees of freedom > no degrees invariant1899 1899 R. A. Lehfeldt Text-bk. Physical Chem. v. 208 Such systems may conveniently be called invariant, univariant, divariant, &c., according as they possess no, one, two, &c., degrees of freedom. 1923 A. C. D. Rivett Phase Rule i. 25 When F = o the system is said to be invariant, since none of its variables may be altered at will without destroying the system in the sense of altering the number of coexisting phases. 1971 F. A. Bettelheim Exper. Physical Chem. xxvii. 259 Phase diagrams of ternary systems that are plotted on a triple co-ordinate graph have two important features: an invariant point, O, and the solubility curves. c. Mathematics and Physics. Unchanged by a specified transformation or operation. Const. under. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > being invariant or covariant invariantive1878 covariant1905 invariant1908 1908 H. Hilton Introd. Theory Groups Finite Order v. 62 If every element of a group G transforms an element g of G into itself, so that g is permutable with every element of G, g is called a normal, self-conjugate, or invariant element of G... Similarly, if every element of G transforms a subgroup H into itself, H is called a normal, self-conjugate, or invariant subgroup of G. 1914 L. Silberstein Theory of Relativity iv. 111 The principle of relativity excludes all such laws as are not invariant with respect to the Lorentz transformation. 1919 A. N. Whitehead Enq. Princ. Nat. Knowl. 39 They [sc. Newton's equations] are invariant for the spatio-temporal transformations from one such set to another within the Newtonian group. 1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra vi. 153 A subgroup S of a group G is normal (in G) if and only if it is invariant under all inner automorphisms of G (i.e., contains with any element all its conjugates). 1955 W. Pauli in W. Pauli Niels Bohr & Devel. Physics 34 The theory is invariant with respect to space or time reflection separately. 1968 Amer. Jrnl. Physics 36 1103/2 The two Einstein postulates state that the laws of physics and speed of light do not change for relatively moving reference systems (being covariant and invariant, respectively). B. n. Mathematics. 1. a. A function of the coefficients of a quantic such that, if the quantic be linearly transformed, the same function of the new coefficients is equal to the first function multiplied by some power of the modulus of transformation. Also attributive. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > invariant resultant1842 invariant1851 catalecticant1852 sextinvariant1852 reciprocant1886 1851 J. J. Sylvester in London, Edinb., & Dublin Philos. Mag. 4th Ser. 2 396 The remaining coefficients are the two well-known hyperdeterminants, or, as I propose henceforth to call them, the two Invariants of the form ax⁴ + 4bx³y + 6cx²y² + 4dxy³ + ey⁴. 1851 J. J. Sylvester in London, Edinb., & Dublin Philos. Mag. 4th Ser. 2 399 If I (a, b,..l) = I (a′, b′,..l′), then I is defined to be an invariant of f. 1873 H. Spencer Study Sociol. (1882) 223 I learn that the Theory of Invariants and the methods of investigation which have grown out of it constitute a step in mathematical progress larger than any made since the Differential Calculus. 1908 J. E. Wright Invariants of Quadratic Differential Forms Pref. The aim of this tract is to give..an account of the invariant theory connected with a single quadratic differential form. 1940 J. L. Coolidge Hist. Geom. Methods ii. ii. 156 The invariant idea, thus launched, was eagerly seized on, especially..by the great twin brethren, Cayley and Sylvester. b. Any quantity or expression which is invariant under a specified transformation or operation. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > invariant under specific operation invariant1908 1908 H. Hilton Introd. Theory Groups Finite Order vii. 99 An expression is an invariant of [a substitution-group] G if it is not altered when we perform on it every one of a set of substitutions which generate G. 1914 L. Silberstein Theory of Relativity iv. 112 It may be expressed shortly by saying that x² + y² + z² — c²t²..is a relativistic invariant. 1956 E. M. Patterson Topol. i. 11 Such entities are called topological invariants, because they are the same for all topologically equivalent spaces. 1959 Chambers's Encycl. I. 260/2 The extensive theory of invariants and covariants has many applications in geometry. 1967 E. U. Condon & H. Odishaw Handbk. Physics (ed. 2) i. x. 144/1 In theory of relativity the distinction between quantities which change with the reference system (covariants) and quantities which do not change with the reference system (invariants) is of paramount importance. 2. gen. An invariant property or feature. ΘΚΠ the world > time > change > absence of change, changelessness > [noun] > something unchanging leopard1382 the law of the Medes and Persiansc1384 constant1832 hardcore1916 invariance1939 invariant1939 facticity1964 1939 Mind 48 39 There is a widespread view that the sole invariant of morals is their sociological function to secure the preservation and welfare of a social group. 1960 K. M. Delavenay & E. Delavenay Introd. Machine Transl. iii. 28 In 1949 Weaver pointed out that..one discovers statistical invariants, as found in cryptography.., semantic invariants,..and logical invariants. 1966 J. J. Katz Philos. Lang. ii. 9 The study of language in general provides us with generalizations expressing the invariant features of language which we may particularize as the requirement that an empirically correct description of a natural language represents such invariants. This entry has not yet been fully updated (first published 1900; most recently modified version published online September 2018). < adj.n.1851
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