Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: MONOMIAL |
MONOMIALAdjective1. Consisting of but a single term or expression. Noun1. A single algebraic expression; that is, an expression unconnected with any other by the sign of addition, substraction, equality, or inequality. |
Crosswords: MONOMIAL |
| English words defined with "MONOMIAL": Monome. (references) |
(From Wikipedia, the free Encyclopedia)
The most obvious fact about monomials is that any polynomial is a linear combination of them, so they can serve as basis vectors in a vector space of polynomials - a fact of constant implicit use in mathematics. An interesting fact from functional analysis is that the full set of monomials tn is not required to span a linear subspace of C[0,1] that is dense for the uniform norm (sharpening the Stone-Weierstrass theorem). It is enough that the sum of the reciprocals n-1 diverge (the Müntz-Szasz theorem).
Notation for monomials is constantly required in fields like partial differential equations. Multi-index notation is helpful: if we write α = (a,b,c) we can define Xα = X1aX2bX3c and save a great deal of space.
In algebraic geometry the varieties defined by monomial equations Xα = 0 for some set of α have special properties of homogeneity. This can be phrased in the language of algebraic groups, in terms of the existence of a group action of an algebraic torus (equivalently by a multiplicative group of diagonal matrices). This area is studied under the name of torus embeddings.
In group representation theory, a monomial representation is a particular kind of induced representation.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Monomial."
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Expression | Frequency per Day |
monomial | 10 |
by monomial multiplying polynomial | 2 |
| Source: compiled by the editor from various references; see credits. | |
| Language | Translations for "MONOMIAL"; alternative meanings/domain in parentheses. | ||||||||||||||||||||||||||||||||||||||||
Albanian | njëgjymtyrësh, njëgjymtyrë. (various references) | ||||||||||||||||||||||||||||||||||||||||
Bulgarian | мономен, моном, едночленен, едночлен. (various references) | ||||||||||||||||||||||||||||||||||||||||
German | eingliedrige Zahlengröße. (various references) | ||||||||||||||||||||||||||||||||||||||||
Greek | μονώνυμοσ. (various references) | ||||||||||||||||||||||||||||||||||||||||
Hebrew | ח" איבר. (various references) | ||||||||||||||||||||||||||||||||||||||||
Hungarian | egytagú szám, egytagú (monosyllabic, one horse). (various references) | ||||||||||||||||||||||||||||||||||||||||
Japanese Kanji | 単 式 . (various references) | ||||||||||||||||||||||||||||||||||||||||
Japanese Katakana | た""うしき. (various references) | ||||||||||||||||||||||||||||||||||||||||
Korean | 단항식. (various references) | ||||||||||||||||||||||||||||||||||||||||
Manx | untermagh. (various references) | ||||||||||||||||||||||||||||||||||||||||
Pig Latin | onomialmay verso de um só pé. (various references) одночлен. (various references) monomski, monom, jednočlan. (various references) monomio. (various references) tek terimli, tek kelimeden oluşan. (various references) одночленний, одночлен. (various references) | ||||||||||||||||||||||||||||||||||||||||
Derivations | |
Words beginning with "MONOMIAL": monomials. (additional references) | |
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"MONOMIAL" is suggested in spellcheckers for the following: Monami, Monoia, Montonhall, Zoonomia. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-i-l-m-m-n-o-o" | |
-2 letters: ammino, ammono, oilman. | |
-3 letters: aloin, amino, amnio, liman, moola, nomoi. | |
-4 letters: amin, ammo, anil, imam, lain, lima, limn, limo, lino, lion, loam, loan, loin, loom, loon, mail, maim, main, malm, mano, milo, mina, moan, moil, mola, momi, mono, mool, moon, nail, naoi, noil, nolo, noma, olio. | |
-5 letters: ail, aim, ain, ami, ani, ion, lam. | |
| Words containing the letters "a-i-l-m-m-n-o-o" | |
+1 letter: monomials. | |
+2 letters: immolation. | |
+3 letters: commonality, immolations. | |
+4 letters: commonalties, emotionalism, malformation, metronomical, monofilament, monomaniacal, monometallic, noncommittal. | |
+5 letters: commonalities, emotionalisms, immunological, malformations, monofilaments, monometallism, monometallist, noncommercial. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
Hexadecimal (or equivalents, 770AD-1900s) (references)4D 4F 4E 4F 4D 49 41 4C |
| Leonardo da Vinci (1452-1519; backwards) (references)
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| American Sign Language (origins from 1620-1817 in Italy and, especially, France) (references)
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| Semaphore (1791, in France) (references)
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| Braille (1829, in France) (references)
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Morse Code (1836) (references)-- --- -. --- -- .. .- .-.. |
| Dancing Men (Sir Arthur Conan Doyle, 1903) (references)
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Binary Code (1918-1938, probably earlier) (references)01001101 01001111 01001110 01001111 01001101 01001001 01000001 01001100 |
HTML Code (1990) (references)M O N O M I A L |
ISO 10646 (1991-1993) (references)004D 004F 004E 004F 004D 0049 0041 004C |
| British Sign Language (Fingerspelling, BSL; 1992, British Deaf Association Dictionary of British Sign Language) (references)
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Encryption (beginner's substitution cypher): (references)4749484947433546 |
| 1. Definition 2. Crosswords 3. Expressions: Internet 4. Translations: Modern | 5. Derivations 6. Anagrams 7. Orthography 8. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
