Definitions

Dimensional

space-time

[speys-tahym]

Single entity that relates space and time in a four-dimensional structure, postulated by Albert Einstein in his theories of relativity. In the Newtonian universe it was supposed that there was no connection between space and time. Space was thought to be a flat, three-dimensional arrangement of all possible point locations, which could be expressed by Cartesian coordinates; time was viewed as an independent one-dimensional concept. Einstein showed that a complete description of relative motion requires equations that include time as well as the three spatial dimensions. He also showed that space-time is curved, which allowed him to account for gravitation in his general theory of relativity.

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Technique used in the physical sciences and engineering to reduce physical properties such as acceleration, viscosity, energy, and others to their fundamental dimensions of length, mass, and time. This technique facilitates the study of interrelationships of systems (or models of systems) and their properties. Acceleration, for example, is expressed as length per unit of time squared; whether the units of length are in the English or metric system is immaterial. Dimensional analysis is often the basis of mathematical models of real situations.

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In operator algebras, an algebra is said to be approximately finite dimensional if it contains an increasing sequence of finite dimensional subalgebras that is dense. One can consider

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