dimensionality

English

Etymology

From dimension +‎ -ality.

Pronunciation

• (Received Pronunciation) IPA^(key): /daɪˌmɛn.ʃəˈnæl.ɪ.tɪ/
• (General American) IPA^(key): /dɪˌmɛn.ʃəˈnæl.ə.tɪ/, [dɪˌmɛn.ʃəˈnæl.ə.ɾɪ], /daɪˌmɛn.ʃəˈnæl.ə.tɪ/, [daɪˌmɛn.ʃəˈnæl.ə.ɾɪ]
• Rhymes: -ælɪti

Noun

dimensionality (plural dimensionalities)

1. The state or characteristic of possessing dimensions.
2. (chiefly mathematics and computing) The number of dimensions 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 [1]:

     That is to say, it is the Analogue of Space, not in the sense in which we formerly regarded Space as the negation of Matter; but in the sense of Infinite Dimensionality, or of Dimensionality in all directions, as a vague generalization from the three spatial dimensions Length, Breadth, and Thickness.

   • 1978, Joseph B. Kruskal, Myron Wish, Multidimensional Scaling‎^[2], →ISBN, page 44:

     This often happens, for example, when a two-dimensional solution is obtained for data whose appropriate dimensionality is higher.

   • 1982, Raoul Bott, Loring W. Tu, Differential Forms in Algebraic Topology‎^[3], →ISBN, page 43:

     Finite Dimensionality of de Rham Cohomology:
     Proposition 5.3.1. If the manifold $M$ 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, page 6 [4]:

     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, doi:10.1007/978-0-387-09823-4, page 142 [5]:

     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).

   • 2010, Basavaraj S. Anami, Shanmukhappa A. Angadi, Sunilkumar S. Manvi, Computer Concepts and C Programming, second, →ISBN, page 139:

     The programming language does not impose any restrictions on the dimensionality of the arrays.

   • 2011, Hermann Moisl, "Hypothesis Generation", chapter 4 in, Warren Maguire and April McMahon, editors, Analysing Variation in English, →ISBN, page 82 [6]:

     A vector $v=(22,38,52,12)$ defines a four-dimensional space with a point at the stated co-ordinates, and so on to any dimensionality $n$. Vector spaces of dimensionality greater than three are impossible to visualise directly […]

Derived terms

• blessing of dimensionality
• curse of dimensionality
• equidimensionality
• four-dimensionality
• pluridimensionality
• three-dimensionality
• unidimensionality

 

Translations

state or characteristic

• Chinese:

  Mandarin: please add this translation if you can

• Finnish: ulotteisuus
• French: dimensionnalité (fr) f
• German: Dimensionalität (de) f
• Japanese: please add this translation if you can
• Romanian: dimensionalitate f
• Swedish: dimensionalitet c

number of dimensions of something

• Finnish: dimensionaalisuus
• French: dimensionnalité (fr) f
• German: Dimensionalität (de) f
• Polish: liczba wymiarów f
• Romanian: dimensionalitate f
• Swedish: dimensionalitet c