Journal ArticleDOI
Kronecker products and matrix calculus in system theory
TLDR
In this article, a review of the algebras related to Kronecker products is presented, which have several applications in system theory including the analysis of stochastic steady state.Abstract:
The paper begins with a review of the algebras related to Kronecker products. These algebras have several applications in system theory including the analysis of stochastic steady state. The calculus of matrix valued functions of matrices is reviewed in the second part of the paper. This calculus is then used to develop an interesting new method for the identifiication of parameters of lnear time-invariant system models.read more
Citations
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Journal ArticleDOI
Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications
TL;DR: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher- order statistics to practical problems is demonstrated.
Journal ArticleDOI
Deconstructing multiantenna fading channels
TL;DR: This work proposes an intermediate virtual channel representation that captures the essence of physical modeling and provides a simple geometric interpretation of the scattering environment and shows that in an uncorrelated scattering environment, the elements of the channel matrix form a segment of a stationary process and that the virtual channel coefficients are approximately uncor related samples of the underlying spectral representation.
Journal ArticleDOI
The ubiquitous Kronecker product
TL;DR: The Kronecker product has a rich and very pleasing algebra that supports a wide range of fast, elegant, and practical algorithms and several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role in the future.
Journal ArticleDOI
Linear transmit processing in MIMO communications systems
TL;DR: The transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power and has similar convergence properties as the receive Wiener filter, i.e., it converges to the matched filter and the zero-forcing filter for low and high signal-to-noise ratio, respectively.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
The matrix minimum principle
TL;DR: The purpose of this paper is to provide an alternate statement of the Pontryagin maximum principle as applied to systems which are most conveniently and naturally described by matrix, rather than vector, differential or difference equations.
Journal ArticleDOI
Analysis and optimization of certain qualities of controllability and observability for linear dynamical systems
P. C. Müller,H. I. Weber +1 more
TL;DR: In this article, the problem of assigning physically meaningful measures of the quality of controllability and observability is considered, and three physical measures-determinant, trace, and maximal eigenvalue of the inverse characteristic controLLability or observability matrix-are imbedded in a set of measures which is defined as the set of certain means related to the eigenvalues of the characteristic matrix.
Journal ArticleDOI
Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products
TL;DR: In this paper, partial derivatives of a matrix function with respect to the elements of the argument matrix are identified. And three definitions of partial derivatives matrices are used, to be denoted by D 1, D 2 and D 3.