Jacobian matrix of a vector function

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


jacobian(v, x)


jacobian(v, x) computes the Jacobian matrix of the vector function with respect to .

If v is a vector then the component ring of v must be a field (i.e., a domain of category Cat::Field) for which differentiation with respect to x is defined.

If v is given as a list of arithmetical expressions, then jacobian returns a matrix with the standard component ring Dom::ExpressionField().


Example 1

The Jacobian matrix of the vector function is:

delete x, y, z:
jacobian([x^3, x*z, y+z], [x, y, z])



A list of arithmetical expressions, or a vector (i.e., an n×1 or 1 ×n matrix of a domain of category Cat::Matrix)


A list of (indexed) identifiers

Return Values

Matrix of the domain Dom::Matrix(R), where R is the component ring of v or the domain Dom::ExpressionField().


For a vector function , where G is a subset of the matrix

is the Jacobian matrix of .

See Also

MuPAD Functions

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