# dimensionality

## English

### 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 and Myron Wish, Multidimensional Scaling, ISBN 0803909403, page 44 [2]:
This often happens, for example, when a two-dimensional solution is obtained for data whose appropriate dimensionality is higher.
• 1982, Raoul Bott and Loring W. Tu, Differential Forms in Algebraic Topology, ISBN 0387906134, page 43 [3]:
Finite Dimensionality of de Rham Cohomology:
Proposition 5.3.1. If the manifold ${\displaystyle M}$ 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 9810222319, 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 9780387098234, 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, and Sunilkumar S. Manvi, Computer Concepts and C Programming, second edition, ISBN 9788120340671, page 139 [6]:
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 9780521898669, page 82 [7]:
A vector ${\displaystyle v=(22,38,52,12)}$ defines a four-dimensional space with a point at the stated co-ordinates, and so on to any dimensionality ${\displaystyle n}$. Vector spaces of dimensionality greater than three are impossible to visualise directly []