Matrix differential calculus with applications to simple, hadamard, and kronecker products
نویسندگان
چکیده
منابع مشابه
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...
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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...
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In this paper we present a brief overview on Hadamard, KhatriRao, Kronecker and several related non-simple matrix products and their properties. We include practical applications, in different areas, of some of the al-
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On the Kronecker Products and Their Applications
This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vecpermutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of...
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ژورنال
عنوان ژورنال: Journal of Mathematical Psychology
سال: 1985
ISSN: 0022-2496
DOI: 10.1016/0022-2496(85)90006-9