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"Matrix calculus" as a book category covers the theory and techniques for differentiating and manipulating functions whose inputs and outputs are vectors and matrices, including rules for gradients, Jacobians, Hessians, matrix and tensor derivatives, and common identities (product, chain, trace, determinant, and elementwise rules). Such books typically develop notation and conventions, show how to derive analytical gradients for optimization problems, and treat topics like matrix differential calculus, vectorization, Kronecker and Hadamard products, and multivariable Taylor expansions. They emphasize applications in machine learning, statistics, optimization, control theory, signal processing, econometrics, and numerical analysis, often connecting hand-derived formulas to automatic differentiation and computational implementation. Target readers range from advanced undergraduates and graduate students to researchers and engineers who need rigorous tools for modeling and computation; most treatments assume familiarity with linear algebra and multivariable calculus and offer worked examples, exercises, and code to bridge theory and practice.

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