Square matrix

About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.

On the generalized Cayley-Hamilton theorem

Abstract: The Cayley-Hamilton theorem is extended to the case where two A and B n \times n matrices are involved. Results similar to the regular case are presented. The results are useful for problems that concern the analysis as well as the synthesis of singular systems, for the definition of a function of two matrices f(A, B) and in various other problems in linear algebra.

Fast computing of the Moore-Penrose inverse matrix

Abstract: In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m ×n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied. is defined. In the case when T is a real m × n matrix, Penrose showed that there is a unique matrix satisfying the four Penrose equations, called the generalized inverse of T. A lot of work concerning generalized inverses has been carried out, in finite and infinite dimension (e.g., (2, 11)). In this article, we provide a method for the fast computation of the generalized inverse of full rank matrices and of square matrices with at least one zero row or column. In order to reach our goal, we use a special type of tensor product of two vectors, that is usually used in infinite dimensional Hilbert spaces. Using this type of tensor product, we also give sufficient conditions for products of square matrices so that the reverse order law for the Moore-Penrose inverse ((1, 4, 5)) is satisfied. There are several methods for computing the Moore-Penrose inverse matrix (cf. (2)). One of the most commonly used methods is the Singular Value Decomposition (SVD) method. This method is very accurate but also time-intensive since it requires a large amount of computational resources, especially in the case of large matrices. In the recent work of P. Courrieu (3), an algorithm for fast computation of Moore- Penrose inverse matrices is presented based on a known reverse order law (eq. 3.2

Realization and Interpolation of Rational Matrix Functions

Abstract: In this paper we generalize for matrix valued functions a number of well known interpolation problems for scalar rational functions and obtain explicit formulas for the solutions The realization approach toward the study of rational matrix functions from systems theory serves here as the main tool The main results recently appeared in the literature; here we give a more systematic and transparent exposition based exclusively on analysis in finite dimensional spaces