Jacobian matrix

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• Jacobian — In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. In algebraic geometry the Jacobian of a curve means the Jacobian variety: a group variety associated to the curve, in which …   Wikipedia

• Matrix calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

• Matrix-free methods — In computational mathematics, a matrix free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix vector… …   Wikipedia

• Jacobian conjecture — In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott Heinrich Keller. It was later named and widely publicised by Shreeram Abhyankar, as an example of a question in …   Wikipedia

• Jacobian — Die Jacobi Matrix (benannt nach Carl Gustav Jacob Jacobi; auch Funktionalmatrix oder Ableitungsmatrix genannt) einer differenzierbaren Funktion ist die Matrix sämtlicher erster partieller Ableitungen. Sie ist eine Darstellungsmatrix, also die… …   Deutsch Wikipedia

• Hessian matrix — In mathematics, the Hessian matrix (or simply the Hessian) is the square matrix of second order partial derivatives of a function; that is, it describes the local curvature of a function of many variables. The Hessian matrix was developed in the… …   Wikipedia

• Generalized Jacobian — In algebraic geometry = In mathematics, there are several notions of generalized Jacobians, which are algebraic groups or complex manifolds that are in some sense analogous to the Jacobian variety of an algebraic curve, or related to the Albanese …   Wikipedia

• P-matrix — In mathematics, a P matrix is a complex square matrix with every principal minor > 0. A closely related class is that of P0 matrices, which are the closure of the class of P matrices, with every principal minor 0. Contents 1 Spectra of P… …   Wikipedia

• Jacobi matrix — may refer to: * Jacobian matrix (matrix of partial derivatives) * A three diagonal symmetric matrix (see orthogonal polynomials) …   Wikipedia

• Z-matrix (mathematics) — In mathematics, the class of Z matrices are those matrices whose off diagonal entries are less than or equal to zero; that is, a Z matrix Z satisfies:Z=(z {ij});quad z {ij}leq 0, quad i eq j.Note that this definition coincides precisely with that …   Wikipedia

• Hurwitz matrix — In mathematics, a square matrix A is called a Hurwitz matrix if every eigenvalue of A has strictly negative real part, that is,:mathop{mathrm{Re [lambda i] < 0, for each eigenvalue lambda i. A is also called a stability matrix, because then the… …   Wikipedia