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