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jinverse

jinverse is a term that does not have a single, universally accepted meaning in mathematics or computer science. It is commonly encountered as a shorthand for the inverse of an entity labeled J, such as a function, matrix, or operator. Depending on the context, jinverse may refer to one of several related concepts.

In mathematics, the inverse of a function J is another function J^{-1} such that J(J^{-1}(x)) = x for

The inverse Jacobian, often denoted J^{-1}, arises in multivariable calculus and numerical methods as the inverse

In software and computational math, some libraries or documentation may expose a function or module named jinverse

Outside formal math, jinverse can also appear as a project name, a variable label, or shorthand in

See also: inverse function, inverse matrix, Jacobian, matrix inversion.

all
x
in
the
domain
of
J^{-1},
and
J^{-1}(J(y))
=
y
for
all
y
in
the
domain
of
J.
If
J
is
represented
by
a
square,
non-singular
matrix,
then
its
inverse
matrix
J^{-1}
exists
and
satisfies
J
J^{-1}
=
J^{-1}
J
=
I.
of
the
Jacobian
matrix
of
a
transformation.
It
is
used
to
transform
differential
changes
between
coordinate
systems
and
in
iterative
methods
such
as
Newton-Raphson
for
systems
of
equations.
that
computes
the
inverse
of
a
square
matrix
or
the
inverse
of
a
transfer
function.
Behavior
depends
on
the
implementation
and
may
raise
an
error
for
singular
inputs.
discussions
where
the
inverse
operation
of
J
is
being
considered.