# A crash course in linear algebra with PyTorch¶

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2024-09-02 16:00:06

We're going to examine each of these concepts with the help of PyTorch, which will also get us familiar with the 'Tensor' object and how it can be used to represent each of the above.

Bascially, a $\textit{vector}$ is a list of numbers. That's it. It's merely a convenient way to represent multiple properties at the same time.

A little more specifically, when we think of a vector (ie. list of numbers), we think of it in the context of all the other vectors (ie. lists of numbers) that have the same length. Note that it's straightforward for us to compare two vectors if they have the same length - for every number in vector $a$ we have a corresponding number from vector $b$, if we just line the vectors up beside each other. We call the set of vectors that all have the same length a $\textit{vector space}$, where the fixed length itself is called the $\textit{dimension}$.

It's appropriate to think of these concepts as an abstraction over your intuition about 3-dimensional space. For that reason, we'll continue this discussion with vectors of length 3 (or less), so that there is always a spatial interpretation.