> For the complete documentation index, see [llms.txt](https://apphp.gitbook.io/artificial-intelligence-with-php/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://apphp.gitbook.io/artificial-intelligence-with-php/machine-learning/mathematics-for-ml/linear-algebra/linear-algebra-in-optimization.md).

# Linear Algebra in Optimization

Finally, linear algebra is crucial in optimizing AI models. The calculation of gradients, which are vectors derived from loss functions with respect to the weights of a model, is performed through linear algebra operations. These gradients are critical in methods such as gradient des