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This article compiles a series of Chinese WeChat posts covering linear algebra, calculus, matrix‑vector differentiation, and Python libraries such as NumPy and SciPy, providing direct links for each topic to help learners deepen their mathematical and programming foundations.
This article explains the definition of matrix‑to‑matrix derivatives, introduces the vectorization‑based differential approach using Kronecker products, presents key matrix‑vectorization properties, and walks through detailed examples illustrating how to compute such derivatives, highlighting their role and limitations in machine‑learning optimization.
This article introduces matrix differential calculus, explains its relationship to scalar and vector differentials, outlines key properties such as addition, multiplication, transpose, trace and determinant rules, and demonstrates how to compute matrix‑vector derivatives using trace tricks.
This article introduces matrix and vector differentiation, explains the nine possible derivative cases, clarifies numerator and denominator layouts, and shows how Jacobian and gradient matrices arise, providing a concise foundation for machine‑learning calculus.