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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". A common data warehouse example involves sales as the measure, with customer and product as dimensions.
Star schema. In computing, the star schema or star model is the simplest style of data mart schema and is the approach most widely used to develop data warehouses and dimensional data marts. [ 1] The star schema consists of one or more fact tables referencing any number of dimension tables. The star schema is an important special case of the ...
The process of dimensional modeling builds on a 4-step design method that helps to ensure the usability of the dimensional model and the use of the data warehouse. The basics in the design build on the actual business process which the data warehouse should cover. Therefore, the first step in the model is to describe the business process which ...
In data warehousing, a fact table consists of the measurements, metrics or facts of a business process. It is located at the center of a star schema or a snowflake schema surrounded by dimension tables. Where multiple fact tables are used, these are arranged as a fact constellation schema. A fact table typically has two types of columns: those ...
The snowflake schema is a variation of the star schema, featuring normalization of dimension tables. In computing, a snowflake schema or snowflake model is a logical arrangement of tables in a multidimensional database such that the entity relationship diagram resembles a snowflake shape. The snowflake schema is represented by centralized fact ...
OLAP cube. An OLAP cube is a multi-dimensional array of data. [1] Online analytical processing (OLAP) [2] is a computer-based technique of analyzing data to look for insights. The term cube here refers to a multi-dimensional dataset, which is also sometimes called a hypercube if the number of dimensions is greater than three.
In a d-dimensional space, Hodge star takes a k-vector to a (dāk)-vector; thus only in d = 3 dimensions is the result an element of dimension one (3ā2 = 1), i.e. a vector. For example, in d = 4 dimensions, the cross product of two vectors has dimension 4ā2 = 2, giving a bivector. Thus, only in three dimensions does cross product define an ...
The table usually lists only one name and symbol that is most commonly used. The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive ), their transformation properties (i.e. whether the quantity is a scalar , vector , matrix or tensor ...