View source for Dimensionality

==English==
{{wikipedia}}

===Etymology===
From {{suffix|en|dimension|ality}}.

===Pronunciation===
* {{IPA|en|/daɪˌmɛn.ʃəˈnæl.ɪ.tɪ/|a=RP}}
* {{IPA|en|/dɪˌmɛn.ʃəˈnæl.ə.tɪ/|[dɪˌmɛn.ʃəˈnæl.ə.ɾɪ]|/daɪˌmɛn.ʃəˈnæl.ə.tɪ/|[daɪˌmɛn.ʃəˈnæl.ə.ɾɪ]|a=GA}}
* {{rhymes|en|ælɪti|s=6}}

===Noun===
{{en-noun}}

# The state or characteristic of possessing dimensions.
# {{lb|en|chiefly|_|mathematics|and|computing}} The number of [[dimension]]s something has.
#* '''1864''', Edward B. Freeland, "Corresponding First Discriminations in Thought and Language", article two of ''The Scientific Universal Language'', as serialized in ''The Continental Monthly'', number 35 (volume 6, number 5), November 1864, bound as ''The Continental Monthly'', volume 6, page 583&nbsp;[http://books.google.com/books?id=w3lBAAAAYAAJ&pg=PA583&dq=dimensionality]:
#*: That is to say, it is the Analogue of Space, not in the sense in which we formerly regarded Space as the ''negation''<!--italics in original--> of Matter; but in the sense of ''Infinite '''Dimensionality'''''<!--itals in orig-->, or of '''Dimensionality''' in all directions, as a vague generalization from the three spatial dimensions ''Length'', ''Breadth'', and ''Thickness''.<!--and again-->
#* {{quote-book|en|year=1978|author=[[w:Joseph Kruskal|Joseph B. Kruskal]]; Myron Wish|title=Multidimensional Scaling|url=http://books.google.com/books?id=ZzmIPcEXPf0C&pg=PA44&dq=dimensionality|page=44|isbn=0803909403
|passage=This often happens, for example, when a two-dimensional solution is obtained for data whose appropriate '''dimensionality''' is higher.}}
#* {{quote-book|en|year=1982|author=w:Raoul Bott; Loring W. Tu|title=Differential Forms in Algebraic Topology|url=http://books.google.com/books?id=S6Ve0KXyDj8C&pg=PA43&dq=dimensionality|page=43|isbn=0387906134
|passage=<u>Finite '''Dimensionality''' of de Rham Cohomology:</u><!--no underlining or colon in original, but it's a heading, which I didn't know how to reproduce here--><br>''Proposition 5.3.1.''<!--preceding was boldfaced not italicized in original; following was italicized--> If the manifold <math>M</math> has a finite good cover, then its cohomology is finite dimensional.}}
#* '''1995''', T. Ogawa, "'''Dimensionality''' and Optical Responses of Materials", chapter 1 in, T. Ogawa and Y. Kanemitsuu, editors, ''Optical Properties of Low-Dimensional Materials'', {{ISBN|9810222319}}, page 6&nbsp;[http://books.google.com/books?id=yToRBYgdMcMC&pg=PA6&dq=bloch]:
#*: As well as the low '''dimensionality''' of the Bloch electron states,{{...}}
#* '''2010''', Lior Rokach and Oded Maimon, "Supervised Learning", chapter 8 in, Oded Maimon and Lior Rokach, editors, ''Data Mining and Knowledge Discovery Handbook'', second edition, {{ISBN|9780387098234}}, [[doi:10.1007/978-0-387-09823-4]], page 142&nbsp;[http://books.google.com/books?id=alHIsT6LBl0C&pg=PA142&dq=dimensionality]:
#*: The difficulties in implementing classification algorithms as is, on high volume databases, derives from the increase in the number of records/instances in the database and of attributes/features in each instance (high '''dimensionality''').
#* {{quote-book|en|year=2010|author=Basavaraj S. Anami; Shanmukhappa A. Angadi; Sunilkumar S. Manvi|title=Computer Concepts and C Programming|pageurl=http://books.google.com/books?id=QqFZ_SPZLJQC&pg=PA139&dq=dimensionality|page=139|publisher=second|isbn=9788120340671
|passage=The programming language does not impose any restrictions on the '''dimensionality''' of the arrays.}}
#* '''2011''', [[w:Hermann Moisl|Hermann Moisl]], "Hypothesis Generation", chapter 4 in, Warren Maguire and April McMahon, editors, ''Analysing Variation in English'', {{ISBN|9780521898669}}, page 82&nbsp;[http://books.google.com/books?id=TjirdzcZKZgC&pg=PA82&dq=dimensionality]:
#*: A vector <math>v=(22,38,52,12)</math> defines a four-dimensional space with a point at the stated co-ordinates, and so on to any '''dimensionality''' <math>n</math>. Vector spaces of '''dimensionality''' greater than three are impossible to visualise directly{{...}}

====Derived terms====
{{col|en|pluridimensionality
|unidimensionality
|equidimensionality
|three-dimensionality
|four-dimensionality
|curse of dimensionality
|blessing of dimensionality}}

====Translations====
{{trans-top|state or characteristic}}
* Chinese:
*: Mandarin: {{t-needed|cmn}}
* Finnish: {{t|fi|ulotteisuus}}
* French: {{t+|fr|dimensionnalité|f}}
* German: {{t+|de|Dimensionalität|f}}
* Japanese: {{t-needed|ja}}
* Romanian: {{t|ro|dimensionalitate|f}}
* Swedish: {{t|sv|dimensionalitet|c}}
{{trans-bottom}}

{{trans-top|number of dimensions of something}}
* Finnish: {{t|fi|dimensionaalisuus}}
* French: {{t+|fr|dimensionnalité|f}}
* German: {{t+|de|Dimensionalität|f}}
* Polish: {{t|pl|liczba wymiarów|f}}
* Romanian: {{t|ro|dimensionalitate|f}}
* Swedish: {{t|sv|dimensionalitet|c}}
{{trans-bottom}}

{{cln|en|6-syllable words}}