In this talk we will discuss the exact eigenvalue distribution 
of the product of independent  rectangular complex Gaussian matrices and 
also that of the product of independent truncated Haar unitary matrices 
and inverses of truncated Haar unitary matrices. The eigenvalues of these 
random matrices form determinantal point processes on the complex plane.  
We will discuss the first example of a random matrix whose eigenvalues 
form a non-rotation invariant determinantal point process on the plane. 
More importantly we will discuss the Jacobian computations for the change 
of variables which enabled the derivation of the exact eigenvalue 
distributions of the above product random matrices.
 
The second theme of this talk is infinite products of random matrices. We 
will discuss the asymptotic behavior of singular values and absolute 
values of eigenvalues of products of i.i.d matrices of fixed size, as the
number of matrices in the product increases to infinity. In the special 
case of isotropic random matrices, We  will discuss the asymptotic joint 
probability density of the singular values and also that of the absolute 
values of eigenvalues of product of right isotropic random matrices. As a 
corollary of these results, we will see that the  probability that all 
the eigenvalues of product of certain i.i.d real random matrices of fixed 
size converges to one, as the number of matrices in the product increases 
to infinity.