# The Spirit of Linear Algebra The Spirit of Linear Algebra is to equally apply to various kind of objects by focusing on what those objects have in common: *addition* and *multiplication* (see more [here](https://youtu.be/yhN_t4Y7-UA?list=PLlXfTHzgMRUKXD88IdzS14F4NxAZudSmv&t=445)). The language parallels what we are talking about! ### Many concepts in linear algebra are inspired by geometry We can note that in linear algebra many ideas and concepts are inspired by geometry. That is we come up with concepts that are applied to vectors, specifically geometric vectors, that have a geometric interpretation in that context. Due to the generality of linear algebra, we can then apply them to elements of, say, $\mathbb{R}^n$ (n tuples). So we have a concept that was intuited via geometry being applied to elements that are not geometric by nature. It is this type of situation that leads many people (myself included) to forget the distinction between the objects we are working with. --- Date: 20220606 Links to: Tags: #review References: * [Linear Algebra 2j: Elements of ℝⁿ as Vectors - So Boring, yet so Important! - YouTube](https://youtu.be/yhN_t4Y7-UA?list=PLlXfTHzgMRUKXD88IdzS14F4NxAZudSmv&t=490)