covariancen.

/kəʊˈvɛːrɪəns/

Etymology: In sense 1 < covariant n. and adj.; in sense 2 < co- prefix 5a + variance n.

1. Mathematics. The property of being covariant; the property of a function of retaining its form when the variables are linearly transformed.

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

discontinuity1803

functionality1857

self-conjugation1866

covariance1878

symmetry1888

monogeneity1906

recursion1913

recursive definition1935

holomorphy1957

unateness1960

the world > relative properties > number > algebra > [noun] > expression > function > covariance or covariant

Jacobian1852

covariant1853

Hessian1856

transmutant1858

transvectant1876

covariance1878

segregate1878

covariancy1895

1878 J. J. Sylvester in Amer. Jrnl. Math. 1 77 It thus appears that every given homogeneous graph has an intrinsic character of capability or incapability of respondence to algebraical in- or co-variance.

1922 E. P. Adams tr. A. Einstein Meaning of Relativity i. 22 We shall also test for co-variance the equations which express the dependence of the stress components of the matter.

1952 C. Møller Theory of Relativity ix. 265 In the special theory of relativity, the covariance of the laws of nature under Lorentz transformations could be very elegantly expressed by means of the four-dimensional tensor calculus.

1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) XI. 436/2 Most physicists agree that any future developments or modifications of Einstein's theory [of relativity] will have to satisfy the principle of covariance.

2. Statistics. The mean value for a population of the product of the deviations of two or more variates from their respective means; it is equal to the correlation coefficient of the variates multiplied by the standard deviation of each variate; analysis of covariance or covariance analysis: an extension of the analysis of variance to investigate and adjust for the dependence of the variate on one or more concomitant observations.

ΘΚΠ

the world > relative properties > number > probability or statistics > [noun] > distribution > variability or spread > measures of > relating to variance

heteroscedasticity1905

homoscedasticity1905

covariance1931

communality1933

principal component1933

1931 A. L. Bailey in Jrnl. Amer. Statist. Assoc. 26 424 (heading) The analysis of covariance.

1931 A. L. Bailey in Jrnl. Amer. Statist. Assoc. 26 424 The term covariance is used here to designate the first product moment, S(x−Mx) (y−My)/N.

1939 C. H. Goulden Methods Statist. Anal. xv. 247 For a single variable the variation is frequently heterogeneous and may be sorted out into components... The same is true for the correlated variability or covariation of two variables, and the mechanism for sorting out the covariance effects is known as the analysis of covariance.

1969 B. E. Cooper Statistics for Experimentalists iv. 44 The covariance between two variables, is a measure of the joint variation between the two variables.

This entry has not yet been fully updated (first published 1972; most recently modified version published online June 2018).

单词	covariance
释义	covariancen. /kəʊˈvɛːrɪəns/ Etymology: In sense 1 < covariant n. and adj.; in sense 2 < co- prefix 5a + variance n. 1. Mathematics. The property of being covariant; the property of a function of retaining its form when the variables are linearly transformed. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > property of discontinuity1803 functionality1857 self-conjugation1866 covariance1878 symmetry1888 monogeneity1906 recursion1913 recursive definition1935 holomorphy1957 unateness1960 the world > relative properties > number > algebra > [noun] > expression > function > covariance or covariant Jacobian1852 covariant1853 Hessian1856 transmutant1858 transvectant1876 covariance1878 segregate1878 covariancy1895 1878 J. J. Sylvester in Amer. Jrnl. Math. 1 77 It thus appears that every given homogeneous graph has an intrinsic character of capability or incapability of respondence to algebraical in- or co-variance. 1922 E. P. Adams tr. A. Einstein Meaning of Relativity i. 22 We shall also test for co-variance the equations which express the dependence of the stress components of the matter. 1952 C. Møller Theory of Relativity ix. 265 In the special theory of relativity, the covariance of the laws of nature under Lorentz transformations could be very elegantly expressed by means of the four-dimensional tensor calculus. 1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) XI. 436/2 Most physicists agree that any future developments or modifications of Einstein's theory [of relativity] will have to satisfy the principle of covariance. 2. Statistics. The mean value for a population of the product of the deviations of two or more variates from their respective means; it is equal to the correlation coefficient of the variates multiplied by the standard deviation of each variate; analysis of covariance or covariance analysis: an extension of the analysis of variance to investigate and adjust for the dependence of the variate on one or more concomitant observations. ΘΚΠ the world > relative properties > number > probability or statistics > [noun] > distribution > variability or spread > measures of > relating to variance heteroscedasticity1905 homoscedasticity1905 covariance1931 communality1933 principal component1933 1931 A. L. Bailey in Jrnl. Amer. Statist. Assoc. 26 424 (heading) The analysis of covariance. 1931 A. L. Bailey in Jrnl. Amer. Statist. Assoc. 26 424 The term covariance is used here to designate the first product moment, S(x−Mx) (y−My)/N. 1939 C. H. Goulden Methods Statist. Anal. xv. 247 For a single variable the variation is frequently heterogeneous and may be sorted out into components... The same is true for the correlated variability or covariation of two variables, and the mechanism for sorting out the covariance effects is known as the analysis of covariance. 1969 B. E. Cooper Statistics for Experimentalists iv. 44 The covariance between two variables, is a measure of the joint variation between the two variables. This entry has not yet been fully updated (first published 1972; most recently modified version published online June 2018). < n.1878
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