vector calculus

Model Perspective

Oct 6, 2022 · Artificial Intelligence

Mastering the Chain Rule for Vector‑to‑Vector and Scalar‑to‑Matrix Derivatives

This article explains the chain rule for vector‑to‑vector derivatives, scalar‑to‑multiple‑vector and scalar‑to‑matrix cases, illustrates how to handle dimensional compatibility, provides concrete examples such as least‑squares optimization, and summarizes four key matrix‑vector derivative conclusions for efficient machine‑learning calculations.

chain rulederivativesmachine learning

0 likes · 5 min read

Mastering the Chain Rule for Vector‑to‑Vector and Scalar‑to‑Matrix Derivatives

Model Perspective

Sep 26, 2022 · Fundamentals

Deriving Scalars with Respect to Vectors Using the Definition Method

This article explains how to compute the derivative of a scalar-valued function with respect to a vector by applying the definition method, illustrating the process with simple and more complex examples, outlining basic differentiation rules, and discussing the limitations of the definition approach for vector‑matrix derivatives.

calculusdefinition methodderivative

0 likes · 6 min read

Deriving Scalars with Respect to Vectors Using the Definition Method