3.1 Mathematical introduction: vector spaces

Abstract:

In this lecture we shall introduce the concept of space-time as a four-dimensional vector space1. Since we live in a three-dimensional Euclidean space, we have a natural tendency to think of this as unique and special. But vectors and many concepts associated with them are not limited by the dimensionality of the space. In the following we denote the number of dimensions of a space byd. Then the hierarchy of the vector spaces is as follows2:

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