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jacobian

Jacobian matrix of a vector function

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Syntax

jacobian(v, x)

Description

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().

Examples

Example 1

The Jacobian matrix of the vector function is:

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

Parameters

v

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

x

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().

Algorithms

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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