November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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G.5 JACOBIAN MATRIX AND THE JACOBIAN
Let 
be M real-valued functions from 
to 
.
Definition: Jacobian Matrix The Jacobian matrix 
contains the following partial derivatives:
(G.36) 
where the argument of 
specifies the independent variables, and thus the elements of the matrix are functions of 
.
Assume that 
is a square matrix.
Definition: Jacobian Determinant The Jacobian determinant (also simply called the Jacobian) of square matrix 
is the following determinant:
(G.37) 
Consider the case of
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