Word
jacobian
Phoneticsja·co·bian
Definition
n. a mathematical grid of derivatives showing how several outputs change when several inputs change at the same time.
n. 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.”
Examples
simple
“Students computed the Jacobian matrix to analyze the multi-joint movements of the robotic arm.”
contextual
“Normalizing flows calculate the determinant of the Jacobian to track how probability density transforms across layers.”
complex
“Regularizing the Frobenius norm of the input-output Jacobian encourages contractive representation learning, enhancing model adversarial robustness.”
Real-World Examples
“The Jacobian matrix collects all first-order partial derivatives of a multivariate function that can be used for backpropagation.” Etymology
Named after German mathematician Carl Gustav Jacob Jacobi (1804–1851), who introduced the functional determinant in 1841.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.
Domains
Scan code
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