Dimension (data warehouse)

A dimension is a structure that categorizes facts and measures in order to enable users to answer business questions. Commonly used dimensions are people, products, place and time.

In a data warehouse, dimensions provide structured labeling information to otherwise unordered numeric measures. The dimension is a data set composed of individual, non-overlapping data elements. The primary functions of dimensions are threefold: to provide filtering, grouping and labelling.

These functions are often described as "slice and dice". Slicing refers to filtering data. Dicing refers to grouping data. A common data warehouse example involves sales as the measure, with customer and product as dimensions. In each sale a customer buys a product. The data can be sliced by removing all customers except for a group under study, and then diced by grouping by product.

A dimensional data element is similar to a categorical variable in statistics.

Typically dimensions in a data warehouse are organized internally into one or more hierarchies. "Date" is a common dimension, with several possible hierarchies:

Dimension (song)

"Dimension" is a song by Australian hard rock band Wolfmother, featured on their 2005 debut studio album Wolfmother. Written by band members Andrew Stockdale, Chris Ross and Myles Heskett, it was released as the second single from the album in Europe (and the third single overall) on 17 April 2006, charting at number 49 on the UK Singles Chart.

Music video

Directed by The Malloys, the music video for "Dimension" was first aired in the week of 13 February 2006. Prior to this, the video was featured on the 2006 extended play (EP) Dimensions.

Critical reception

In a review of Wolfmother for Blender, writer Jonah Weiner identified "Dimension" as an example of the band "at [their] hardest", describing it as an "acid anthem".NME reviewer James Jam described the song as "a throb of gonzo metal not unlike Black Sabbath playing Motown".

Track listing

All songs written and composed by Andrew Stockdale, Chris Ross, Myles Heskett. 

References

Krull dimension

In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.

The Krull dimension has been introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal I in a polynomial ring R is the Krull dimension of R/I.

A field k has Krull dimension 0; more generally, k[x₁, ..., x_n] has Krull dimension n. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.

Explanation

We say that a chain of prime ideals of the form has length n. That is, the length is the number of strict inclusions, not the number of primes; these differ by 1. We define the Krull dimension of to be the supremum of the lengths of all chains of prime ideals in .

Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say V is finite-dimensional if the dimension of V is finite, and infinite-dimensional if its dimension is infinite.

The dimension of the vector space V over the field F can be written as dim_F(V) or as [V : F], read "dimension of V over F". When F can be inferred from context, dim(V) is typically written.

Examples

The vector space R³ has

as a basis, and therefore we have dim_R(R³) = 3. More generally, dim_R(Rⁿ) = n, and even more generally, dim_F(Fⁿ) = n for any field F.

The complex numbers C are both a real and complex vector space; we have dim_R(C) = 2 and dim_C(C) = 1. So the dimension depends on the base field.

The only vector space with dimension 0 is {0}, the vector space consisting only of its zero element.

Dimension (shampoo)

Dimension Shampoo was a heavily perfumed shampoo product, which was produced in the early 1980s. This was by the personal products division of Lever Brothers, and marketed by Ogilvy. The shampoo came in a distinctive dark yellow bottle, and left a strong muskone and civetone aroma on the hair. There was also a companion conditioner marketed with this product. It has been stated by many previous users of dimension shampoo that it caused their hair to fall out, due to the extreme astringency of the product.

On April 18, 1985, Lever Brothers reorganized their marketing structure and moved their personal products division business to J. Walter Thompson.

At the time, Dimension was a highly popular brand. (Lever spent an estimated $12.5M in advertising the brand in 1984.) However, shortly after Lever's marketing reorganization, Dimension ran-out on store shelves, and never returned. Lever Brothers never made any public explanation for the disappearance of the product; although they referred to the marketing reorganization as a consolidation of the personal products brands, and stated that the decision in-part had to do with its plans for international marketing.

Dithiopyr

Dithiopyr is a chemical used as an preemergent herbicide used to prevent crabgrass seeds from sprouting in the spring. Dithiopyr may alter microtubule polymerization and stability by "interacting with microtubule associated proteins or microtubule organizing centers rather than interaction directly with tubulin."

It is an ingredient in many products including Dimension from Dow AgroSciences.

Synthesis

References