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"Matrix differential calculus" as a book category covers the theory, notation, and computational techniques for taking derivatives when variables are vectors and matrices rather than scalars. Books in this genre present matrix- and tensor-valued analogues of gradients, Jacobians, Hessians, directional derivatives and chain rules; they develop tools such as vectorization, Kronecker products, index notation, and matrix identities; and they show how to manipulate and simplify expressions for derivatives in compact, matrix-based form. Typical treatments range from formal proofs and coordinate-free approaches to hands-on recipes for computing gradients and Hessians in statistics, optimization, machine learning, control theory, and econometrics. Intended readers are advanced undergraduates, graduate students, and practitioners with a background in linear algebra and multivariable calculus who need a rigorous reference or practical guide for deriving and implementing matrix-based derivative formulas.

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