# Jacobian

CEFR C2 · Noun

Source: https://englishreference.com/word/jacobian
Updated: 2026-09-28

## Definition

a mathematical grid of derivatives showing how several outputs change when several inputs change at the same time.

For teachers: the matrix of all first-order partial derivatives of a vector-valued function, representing its best linear approximation near a point.

## Examples

- Students computed the Jacobian matrix to analyze the multi-joint movements of the robotic arm.
- Normalizing flows calculate the determinant of the Jacobian to track how probability density transforms across layers.
- Regularizing the Frobenius norm of the input-output Jacobian encourages contractive representation learning, enhancing model adversarial robustness.

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