Jacobian matrix and determinant
In vector calculus, the Jacobian matrix (/dʒᵻˈkoʊbiən/, /jᵻˈkoʊbiən/) is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square matrix, both the matrix and its determinant are referred to as the Jacobian in literature. Suppose f : ℝn → ℝm is a function which takes as input the vector x ∈ ℝn and produces as output the vector f(x) ∈ ℝm. Then the Jacobian matrix J of f is an m×n matrix, usually defined and arranged as follows: or, component-wise: These concepts are named after the mathematician Carl Gustav Jacob Jacobi (1804–1851).
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix (/dʒᵻˈkoʊbiən/, /jᵻˈkoʊbiən/) is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square matrix, both the matrix and its determinant are referred to as the Jacobian in literature. Suppose f : ℝn → ℝm is a function which takes as input the vector x ∈ ℝn and produces as output the vector f(x) ∈ ℝm. Then the Jacobian matrix J of f is an m×n matrix, usually defined and arranged as follows: or, component-wise: These concepts are named after the mathematician Carl Gustav Jacob Jacobi (1804–1851).
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25بك المحتوى هنا ينقصه الاستشه ...... ضيات كارل غوستاف جاكوب جاكوبي.
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A Matriz Jacobiana (denominado ...... as derivadas parciais existam.
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De jacobi-matrix van een funct ...... ix van als volgt gedefinieerd:
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Die Jacobi-Matrix (benannt nac ...... Funktionen in der Mathematik.
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En analyse vectorielle, la mat ...... on de problèmes non linéaires.
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En cálculo vectorial, se llama ...... e la curva puede ser embebida.
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In analisi matematica, in part ...... riali di variabile vettoriale.
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In vector calculus, the Jacobi ...... stav Jacob Jacobi (1804–1851).
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Macierz Jacobiego – macierz zb ...... danym punkcie, o ile istnieje.
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Матрица Яко́би отображения в т ...... вольного отображения в точке .
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25بك المحتوى هنا ينقصه الاستشه ...... ضيات كارل غوستاف جاكوب جاكوبي.
@ar
A Matriz Jacobiana (denominado ...... as derivadas parciais existam.
@pt
De jacobi-matrix van een funct ...... ix van als volgt gedefinieerd:
@nl
Die Jacobi-Matrix (benannt nac ...... Funktionen in der Mathematik.
@de
En analyse vectorielle, la mat ...... on de problèmes non linéaires.
@fr
En cálculo vectorial, se llama ...... e la curva puede ser embebida.
@es
In analisi matematica, in part ...... to a Carl Gustav Jacob Jacobi.
@it
In vector calculus, the Jacobi ...... stav Jacob Jacobi (1804–1851).
@en
Macierz Jacobiego – macierz zb ...... danym punkcie, o ile istnieje.
@pl
Матрица Яко́би отображения в т ...... вольного отображения в точке .
@ru
label
Jacobi-Matrix
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Jacobi-matrix
@nl
Jacobian matrix and determinant
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Jacobiano
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Macierz Jacobiego
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Matrice jacobiana
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Matrice jacobienne
@fr
Matriz jacobiana
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Матрица Якоби
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مصفوفة جاكوبية ومحددة جاكوبية
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