linalg::jacobian -- Jacobian
matrix of a vector function
Introductionlinalg::jacobian(v, x) computes the
Jacobian matrix of the vector function v with respect to
x.
Call(s)linalg::jacobian(v, x)
Parametersv |
- | 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 |
Returnsa matrix of the domain Dom::Matrix(R), where R is
the component ring of v or the domain
Dom::ExpressionField().
Related
Functions
Detailsv 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.v is given as a list of arithmetical expressions,
then linalg::jacobian returns a matrix with the standard
component ring Dom::ExpressionField().
Example
1The 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
+- -+
| diff(v1(x),x1) ... diff(v1(x),xn) |
| |
Jv(x):= | : : |
| |
| diff(vm(x),x1) ... diff(vm(x),xn) |
+- -+
is the Jacobian matrix of v.