Jacobian

From Jacobi +‎ -an, after Carl Gustav Jacob Jacobi, a German mathematician of the 19th century.

• enPR: yä-kō'-bi-un, IPA^(key): /jɑːˈkəʊ.bi.ən/
• IPA^(key): /d͡ʒəˈkoʊ.bi.ən/

• Audio (US):

  (file)

Jacobian (not comparable)

1. Used to specify certain mathematical objects named in honour of C. G. J. Jacobi.

   The Jacobian matrix has partial derivatives as its entries.

Jacobian (plural Jacobians)

1. (calculus) A Jacobian matrix or its associated operator.
   • 2016, Kyle E. Niemeyer, Nicholas J. Curtis, Chih-Jen Sung, “pyJac: analytical Jacobian generator for chemical kinetics”, in arXiv‎^[1]:

     As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation, then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons..

2. (calculus) The determinant of such a matrix.
   • 2015, Ping Ngai Chung, Craig Costello, Benjamin Smith, “Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes”, in arXiv‎^[2]:

     In terms of per-bit security, elliptic curves and Jacobians of genus 2 curves appear to be roughly equivalent. However, when it comes to efficient and side-channel-aware implementations, we see a curious divergence.

• Jacobian on Wikipedia.Wikipedia

From Jacob +‎ -ian.

Jacobian (comparative more Jacobian, superlative most Jacobian)

1. Of or relating to the biblical Jacob.

   Synonym: Jacobic

• Bajocian