This year I've working on gaining a deeper understanding of AI and ML tools. To do this I've been studying a lot of math, specifically vector spaces (opens in a new tab). As I've been getting increasingly excited about the progress I'm making, I figured some blog posts were in my future. This seemed like a good enough reason to go on a side quest to set up equation rendering.
Fortunately, the blogging framework I'm using right now, Nextra (opens in a new tab), comes with (nice) support built in. After migrating some configuration files, I was able get it set up and wanted to do a "little hello" world post with some equations!
So, as a proof-of-concept, here is the definition a subspace, of a core concept I've been studying in Sheldon Axler's text Linear Algebra Done Right (opens in a new tab).
For a vector space over a field (nominally either the real numbers or the complex numbers), the subset is said to be a subspace of V if and only if () the following 3 conditions are met:
- Additive Identity: The additive identity is also . That is, , where is an element in such that for all .
- Closure Under Addition: For any we also have .
- Closure Under Scalar Multiplication: For and we have .
Update 2023-06-25: Fixed the definition of a subspace to include the trivial case i.e. instead of . Thanks Dad :)
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