> 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/scalars.md). # Scalars ### Scalars in Linear Algebra Scalars are fundamental elements in linear algebra. They are single numerical values, typically real or complex numbers, that play a crucial role in vector and matrix operations. Unlike vectors or matrices, which represent multiple values or elements, scalars are single-valued quantities. In linear algebra, scalars are used to scale vectors, multiply matrices, and perform various other operations that form the basis of many mathematical and practical applications. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://apphp.gitbook.io/artificial-intelligence-with-php/machine-learning/mathematics-for-ml/linear-algebra/scalars.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.