Sometimes you're working with code that does maths and you just need that one formula, or proof, from linear algebra. It tends to pop up a lot in custom deep learning code, physical simulations or novel machine learning tricks. In these cases, try searching for "the matrix cookbook". It will take you to a hosted pdf that contains many of the formulas you might need.
The book contains proofs and formulas that involve:
- matrix inversion
- matrices with complex numbers
- decomposition proofs
- probability distributions in higher dimensions
The cookbook is not meant for beginners. You really need to have taken a full course in linear algebra and probability theory to appreciate everything. But it's proven to be one of those books that can prevent a google-search.
Let's say you appreciate a reminder on the conditional distribution of the Gaussian. Then on page 40, on section 8.1.3 you'll find:
The next page lists:
The matrix cookbook is mathematically dense. It certainly expects that you're mathematically experienced. But if you are, it's a nice reference to have. If you're interested you can download it from the university of Waterloo.
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