I’m not referring to the idea of arrows in space with direction and magnitude, but vectors as in a Mathematical sense. This article explores the notion of vectors, which will then be extended to Tensors. Of course, as this is intended for a basic understanding, it will lack Mathematical rigor.
What is a Vector?
A vector is an element of a set. This set is called a Vector space. In order for a Set to qualify as a Vector space, it need to satisfy certain conditions. Refer this link for a detailed description. To summarize, a vector space V over a Scalar Field F is a set for which operation of additions and scalar multiplication is defined with following properties: