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linalg::jacobian -- Jacobian matrix of a vector function

Introduction

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

Call(s)

linalg::jacobian(v, x)

Parameters

v - a list of arithmetical expressions, or a vector (i.e., an n x 1 or 1 x n matrix of a domain of category Cat::Matrix)
x - a list of (indexed) identifiers

Returns

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

Related Functions

linalg::hessian, linalg::grad

Details

Example 1

The Jacobian matrix of the vector function v=[x^3, x*y, y+z] is:

>> delete x, y, z:
   linalg::jacobian([x^3, x*z, y+z], [x, y, z])
                             +-            -+
                             |     2        |
                             |  3 x , 0, 0  |
                             |              |
                             |    z,  0, x  |
                             |              |
                             |    0,  1, 1  |
                             +-            -+

Background




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