semi-invariantn.

Forms: Also seminvariant.

Etymology: < semi- prefix + invariant adj. and n.Previous versions of the OED give the stress as: semi-inˈvariant.

Mathematics.

1. A function of the coefficients of a binary quantic which remains unchanged, except for a constant factor, when x + λ is substituted for x, but not when y + λ is substituted for y.

ΘΚΠ

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

peninvariant1860

semi-invariant1860

perpetuant1882

subinvariant1882

syzygant1882

1860 in Cayley Math. Papers (1891) IV. 241 The coefficients of the equation of differences, quâ functions of the differences of the roots of the given equation, are leading coefficients of covariants, or (to use a shorter expression) they are ‘Seminvariants’. [Note, The term ‘Seminvariant’ seems to me preferable to M. Brioschi's term ‘Peninvariant’.]

1882 J. J. Sylvester in Amer. Jrnl. Math. 5 79 On Sub~invariants, i.e. Semi-Invariants to Binary Quantics of an Unlimited Order.

2. Statistics. Any of a set of functions of a statistical distribution, each expressible as a polynomial in the moments.

ΚΠ

1903 T. N. Thiele Theory of Observations vi. 24 From the sums of powers we can easily compute also another serviceable collection of symmetrical functions, which for brevity we shall call the half-invariants.]

1922 A. Fisher Math. Theory Probabilities (ed. 2) xiv. 191 (heading) Semi-invariants of Thiele.

1930 Biometrika 22 225 Thiele, in 1889, after defining the semi-invariants, used symmetric functions of the observations of a sample which are the same functions of the sample moment coefficients as the population semi-invariants are of the population moment coefficients. He supplied an expression covering all the semi-invariants of the mean.

1968 P. A. P. Moran Introd. Probability Theory vi. 267 The κ_n (n ≥ 2) are dependent only on μ₂, μ₃,..and are the same for all distributions of the form F(x + d) (—∞ < d < ∞). They are therefore sometimes known as ‘semi-invariants’ since they are invariant under translation.

This entry has not yet been fully updated (first published 1986; most recently modified version published online December 2020).

单词	semi-invariant
释义	semi-invariantn. Forms: Also seminvariant. Etymology: < semi- prefix + invariant adj. and n.Previous versions of the OED give the stress as: semi-inˈvariant. Mathematics. 1. A function of the coefficients of a binary quantic which remains unchanged, except for a constant factor, when x + λ is substituted for x, but not when y + λ is substituted for y. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > invariant > semi-invariant peninvariant1860 semi-invariant1860 perpetuant1882 subinvariant1882 syzygant1882 1860 in Cayley Math. Papers (1891) IV. 241 The coefficients of the equation of differences, quâ functions of the differences of the roots of the given equation, are leading coefficients of covariants, or (to use a shorter expression) they are ‘Seminvariants’. [Note, The term ‘Seminvariant’ seems to me preferable to M. Brioschi's term ‘Peninvariant’.] 1882 J. J. Sylvester in Amer. Jrnl. Math. 5 79 On Sub~invariants, i.e. Semi-Invariants to Binary Quantics of an Unlimited Order. 2. Statistics. Any of a set of functions of a statistical distribution, each expressible as a polynomial in the moments. ΚΠ 1903 T. N. Thiele Theory of Observations vi. 24 From the sums of powers we can easily compute also another serviceable collection of symmetrical functions, which for brevity we shall call the half-invariants.] 1922 A. Fisher Math. Theory Probabilities (ed. 2) xiv. 191 (heading) Semi-invariants of Thiele. 1930 Biometrika 22 225 Thiele, in 1889, after defining the semi-invariants, used symmetric functions of the observations of a sample which are the same functions of the sample moment coefficients as the population semi-invariants are of the population moment coefficients. He supplied an expression covering all the semi-invariants of the mean. 1968 P. A. P. Moran Introd. Probability Theory vi. 267 The κ_n (n ≥ 2) are dependent only on μ₂, μ₃,..and are the same for all distributions of the form F(x + d) (—∞ < d < ∞). They are therefore sometimes known as ‘semi-invariants’ since they are invariant under translation. This entry has not yet been fully updated (first published 1986; most recently modified version published online December 2020). < n.1860
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