Jacobian matrix and determinant

In vector calculus, the Jacobian matrix (/əˈkbiən/,[1][2][3] /ɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature.[4] They are named after Carl Gustav Jacob Jacobi.

  1. ^ "Jacobian - Definition of Jacobian in English by Oxford Dictionaries". Oxford Dictionaries - English. Archived from the original on 1 December 2017. Retrieved 2 May 2018.
  2. ^ "the definition of jacobian". Dictionary.com. Archived from the original on 1 December 2017. Retrieved 2 May 2018.
  3. ^ Team, Forvo. "Jacobian pronunciation: How to pronounce Jacobian in English". forvo.com. Retrieved 2 May 2018.
  4. ^ W., Weisstein, Eric. "Jacobian". mathworld.wolfram.com. Archived from the original on 3 November 2017. Retrieved 2 May 2018.{{cite web}}: CS1 maint: multiple names: authors list (link)

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