Seven-dimensional space

In physics and maths, a sequence of n number can also be understood as a location in n-dimensional space. When n = 7, the set of all such locations is called 7-dimensional Euclidean space. Seven-dimensional elliptically and hyperbolic space are also studied, with constant positive and negative curvature.
Abstract seven-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe in which we live is somehow seven-dimensional (or indeed higher) is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics, but it does not matter for mathematics.
Formally, seven-dimensional euclidean space is generated by considering all real 7-tuple as 7-vector in this space. As such it has the properties of all Euclidean spaces, so it is linear, has a metric and a full set of vector operations. In particular the dot product between two 7-vectors is readily defined, and can be used to calculate the metric. 7 × 7 matrix can be used to describe transformations such as rotation which keep the origin fixed.