Cheat sheet for matrix calculus

Description

Dear Reviewer: I am the sole author of the attached mathematics notes. This document was created using LaTeX, the standard typesetting system for technical and scientific documentation in academia. LaTeX excels at rendering complex mathematical notation with precision - a capability that makes it indispensable for researchers, mathematicians, and engineering professionals. The PDF you receive is compiled directly from my LaTeX source files, which I can provide upon request for verification purposes. The notes focus on Matrix Calculus, an advanced mathematical technique essential for solving high-level problems in machine learning, econometrics, and physics. While this topic is critically important in technical courses and research, comprehensive learning resources remain scarce compared to its foundational counterparts. My notes systematically organize key theorems, derivative rules, and practical applications that I developed during my PhD studies. By sharing this compilation, I aim to help fellow learners overcome common challenges in: The note included the commonly-used techniques related to calculus in matrix and the relationship with algebra, which is useful while dealing with the advanced topic in economics, statistical questions and mathematical theorem related to multivariate modeling. Topic list: 1. Introduction 2. Notation and Nomenclature 3. Matrix Multiplication 4. Partioned Matrices 5. Matrix Differentiation (with practice examples and 15 propositions) 6. References