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Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
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59 citations
TL;DR: In this paper, a simple recursive scheme for parametrization of n-by-n unitary matrices is presented, which is expressed as a product containing the (n−1)-by-(n− 1) matrix and a unitary matrix that contains the additional parameters needed to go from n−1 to n.
Abstract: A simple recursive scheme for parametrization of n-by-n unitary matrices is presented. The n-by-n matrix is expressed as a product containing the (n−1)-by-(n−1) matrix and a unitary matrix that contains the additional parameters needed to go from n−1 to n. The procedure is repeated to obtain recursion formulas for n-by-n unitary matrices.
59 citations
TL;DR: In this paper, the convex conical hull of the rows of an m X n matrix A is defined as a convex convex hull for which the nonnegative orthant is present.
Abstract: Collatz [2, Chap. 3, ?23] treats square matrices of monotone kind and shows that for such matrices the above implication is equivalent to: A-' exists and A1 2 0.1 Matrices of monotone kind have useful applications in numerical analysis [2, Chap. 3], [7]. It is the purpose of this note to generalize Collatz's result to rectangular matrices, and also to show that, for the general rectangular case, a matrix of monotone kind can be further characterized as one for which the convex conical hull of the rows contains the nonnegative orthant. (For an m X n matrix A, the convex conical hull of the rows of A is defined as
59 citations
Posted Content•
01 Jan 2001
TL;DR: The -qap-command as discussed by the authors implements the quadratic assignment procedure (QAP) and allows running any estimation command using QAP samples, which is a resampling-based method for calculating the correct standard errors.
Abstract: Some data sets contain observations corresponding to pairs of entities (people, companies, countries, etc.). Conceptually, each observation corresponds to a cell in a square matrix, where the rows and columns are labelled by the entities. For example, consider a square matrix where the rows and columns are the 50 U.S. states. Each observation would contain numbers such as the distance between the pair of states, exports from one state to the other, etc. The observations are not independent, so estimation procedures designed for independent observations will calculate incorrect standard errors. The quadratic assignment procedure (QAP), which is commonly used in social network analysis, is a resampling-based method, similar to the bootstrap, for calculating the correct standard errors. This talk explains the QAP algorithm and describes the -qap- command, with syntax similar to -bstrap- command, which implements the quadratic assignment procedure and allows running any estimation command using QAP samples.
59 citations
TL;DR: It is proved that a companion matrix is similar to a diagonal matrix or Jordan matrix, and the transformation matrices between them are given and the similarity transformation and the companion matrix to system identification are applied.
Abstract: Special matrices are very useful in signal processing and control systems. This paper studies the transformations and relationships between some special matrices. The conditions that a matrix is similar to a companion matrix are derived. It is proved that a companion matrix is similar to a diagonal matrix or Jordan matrix, and the transformation matrices between them are given. Finally, we apply the similarity transformation and the companion matrix to system identification.
58 citations