# Jacobian

> Source: https://sukruyusufkaya.com/en/glossary/jacobian
> Updated: 2026-05-13T20:59:37.042Z
> Type: glossary
> Category: matematik-istatistik-optimizasyon
**TLDR:** A matrix structure that carries derivative information for vector-valued functions.

<p>The Jacobian is a matrix that systematically represents the derivative structure of multivariable, vector-valued functions. Each row and column summarizes how one output changes with respect to one input. This structure is important for understanding local transformation behavior, performing coordinate changes, and analyzing multidimensional systems. The Jacobian appears frequently in deep learning, control theory, robotics, and differentiable systems. It is especially powerful for understanding precise change relationships.</p>