Calculus of Exponential Matrix with Kronecker Product

On Kronecker products, tensor products and matrix differential calculus

The algebra of the Kronecker products of matrices is recapitulated using a notation that reveals the tensor structures of the matrices. It is claimed that many of the difficulties that are encountered in working with the algebra can be alleviated by paying close attention to the indices that are concealed beneath the conventional matrix notation. The vectorisation operations and the commutation...

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Shifted Kronecker Product Systems

Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker struct...

Matrix Differential Calculus with Applications to Simple, Hadamard, and Kronecker Products

Several definitions are in use for the derivative of an mx p matrix function F(X) with respect to its n x q matrix argument X. We argue that only one of these definitions is a viable one, and that to study smooth maps from the space of n x q matrices to the space of m x p matrices it is often more convenient to study the map from nq-space to mp-space. Also, several procedures exist for a calcul...

Transformation of the Kronecker Product