majorizev.

Brit.

/ˈmeɪdʒərʌɪz/, U.S.

/ˈmeɪdʒərˌaɪz/

Forms: 1800s– majorize, 1900s– majorise.

Origin: Formed within English, by derivation. Etymons: major n.¹, -ize suffix.

Etymology: < major n.¹ + -ize suffix.

†1. intransitive. To attain (one's) majority; to come of age. Obsolete. rare.

ΘΚΠ

the world > people > person > adult > be adult [verb (intransitive)] > become adult

win of elda1300

throc1325

to grow up1535

discradle1634

to run up1713

mature1844

majorize1896

1896 C. F. Keary Herbert Vanlennert i. 5 I didn't know you had regularly come of age..I imagined that you didn't majorize till twenty-five or something of that sort.

†2. intransitive. Rugby. To convert a try into a goal. Now disused.

ΘΚΠ

society > leisure > sport > types of sport or game > ball game > football > rugby football > play rugby football [verb (transitive)] > score

pot1856

secure1866

convert1896

goal1900

majorize1904

to dot down1956

1904 in N.E.D. Majorize,..To convert a try into a goal, i.e. to increase the points from three to five.

3. transitive. Music. To put into a major key. rare.

ΚΠ

1927 Musical Times Nov. 1040 So monotonous a thing as to majorise every cadence.

4. transitive. Mathematics. Of a function, set element, etc.: to dominate or have precedence over (another mathematical entity of the same type) according to a particular criterion (esp. one which defines a partial ordering). Cf. majorant n.

ΚΠ

1934 G. H. Hardy et al. Inequalities ii. 45 We say that (α′) is majorised by (α), and write (α′) ≺ (α), when (α) and (α′) can be arranged so as to satisfy the following three conditions: [etc.].

1968 Proc. Koninkl. Nederlandse Akad. van Wetenschappen A. 71 431 The partial order is..defined by writing g ≺ f whenever ∫s0g^* ≤ ∫s0f^*∫10g^* = ∫10f^*. Then fis said to majorize g.

1979 Proc. London Math. Soc. 38 304 The integral..is majorized by (A‖f‖^*_λ,q)^q.

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xviii. 392 A series whose terms are not smaller than those of a given series with positive terms is said to dominate or majorize the given series.

1991 Oxf. Econ. Papers 43 221 The concept of ‘majorization’ is useful as a partial ordering for the degree of heterogeneity. Let v = (v₁,…v_n) and v′ = (v′₁,…v′_n). Then v′ is said to majorize v if, and only if, there exists a doubly stochastic matrix P such that v = Pv′. Thus if the set of values v can be represented as a weighted average of the set of values v′, then thes set v′ is more heterogeneous than v.

This entry has been updated (OED Third Edition, June 2000; most recently modified version published online March 2022).

单词	majorize
释义	majorizev. Brit. /ˈmeɪdʒərʌɪz/, U.S. /ˈmeɪdʒərˌaɪz/ Forms: 1800s– majorize, 1900s– majorise. Origin: Formed within English, by derivation. Etymons: major n.¹, -ize suffix. Etymology: < major n.¹ + -ize suffix. †1. intransitive. To attain (one's) majority; to come of age. Obsolete. rare. ΘΚΠ the world > people > person > adult > be adult [verb (intransitive)] > become adult win of elda1300 throc1325 to grow up1535 discradle1634 to run up1713 mature1844 majorize1896 1896 C. F. Keary Herbert Vanlennert i. 5 I didn't know you had regularly come of age..I imagined that you didn't majorize till twenty-five or something of that sort. †2. intransitive. Rugby. To convert a try into a goal. Now disused. ΘΚΠ society > leisure > sport > types of sport or game > ball game > football > rugby football > play rugby football [verb (transitive)] > score pot1856 secure1866 convert1896 goal1900 majorize1904 to dot down1956 1904 in N.E.D. Majorize,..To convert a try into a goal, i.e. to increase the points from three to five. 3. transitive. Music. To put into a major key. rare. ΚΠ 1927 Musical Times Nov. 1040 So monotonous a thing as to majorise every cadence. 4. transitive. Mathematics. Of a function, set element, etc.: to dominate or have precedence over (another mathematical entity of the same type) according to a particular criterion (esp. one which defines a partial ordering). Cf. majorant n. ΚΠ 1934 G. H. Hardy et al. Inequalities ii. 45 We say that (α′) is majorised by (α), and write (α′) ≺ (α), when (α) and (α′) can be arranged so as to satisfy the following three conditions: [etc.]. 1968 Proc. Koninkl. Nederlandse Akad. van Wetenschappen A. 71 431 The partial order is..defined by writing g ≺ f whenever ∫s0g^* ≤ ∫s0f^∫10g^ = ∫10f^. Then fis said to majorize g. 1979 Proc. London Math. Soc.* 38 304 The integral..is majorized by (A‖f‖^_λ,q)^q. 1989 W. Gellert et al. VNR Conc. Encycl. Math.* (ed. 2) xviii. 392 A series whose terms are not smaller than those of a given series with positive terms is said to dominate or majorize the given series. 1991 Oxf. Econ. Papers 43 221 The concept of ‘majorization’ is useful as a partial ordering for the degree of heterogeneity. Let v = (v₁,…v_n) and v′ = (v′₁,…v′_n). Then v′ is said to majorize v if, and only if, there exists a doubly stochastic matrix P such that v = Pv′. Thus if the set of values v can be represented as a weighted average of the set of values v′, then thes set v′ is more heterogeneous than v. This entry has been updated (OED Third Edition, June 2000; most recently modified version published online March 2022). < v.1896
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