https://signal-and-syntax.com/tags/linear-algebra/Recent content in Linear Algebra on Signal & SyntaxHugoen-usTue, 07 Oct 2025 06:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-think/Tue, 07 Oct 2025 06:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-think/When you enter a sentence into a Large Language Model (LLM) such as ChatGPT or Claude , the model does not process words as language. It represents them as numbers. Each word, phrase, and code token becomes a vector — a list of real-valued coordinates within a high-dimensional space. Relationships between meanings are captured not by grammar or logic but by geometry. The closer two vectors lie, the more similar their semantic roles appear to the model.https://signal-and-syntax.com/posts/python-sympy-vs-numpy/Fri, 05 Sep 2025 11:45:00 -0700https://signal-and-syntax.com/posts/python-sympy-vs-numpy/Most of us reach for NumPy whenever math shows up in a project. But sometimes, you don’t want approximate answers, you want exact math. That’s when you pull SymPy out of your programmer’s toolkit and get to work. It’s easy to think of SymPy only in academic terms, like running physics simulations where small rounding errors can snowball into nonsense, or checking algebraic identities where a value such as 0.0000001 should really be treated as exactly 0.