New method for general Kennaugh's pseudo-eigenvalue equation in radar polarimetry
type: Item
instance of: scholarly article
title: New method for general Kennaugh's pseudo-eigenvalue equation in radar polarimetry
zbMATH Open document ID: 1262.15009
author: Sitao Ling
author: Tongsong Jiang
published in: Frontiers of Mathematics in China
publication date: 2012-11-15T00:00:00Z
review text: This paper studies the Kennaugh pseudo-eigenvalue equation \( Sx = \lambda x^*\) that is basic to radar polarimetry. This equation involves the coneigenvalues of \(S\) and it can be rephrased in a Gaussian normal equations way as \(SS^*x = |\lambda|^2x\). Thus with \(A = SS^*\) it becomes a special case of \[ AX^* - XB = O_n \;. \tag{\(*\)} \] This latter equation has been studied extensively and for varying right hand sides \(C\). The authors replace \(A_{n,n} = A_1 + iA_2\) by its real representation \(A_\sigma = \left( \begin{matrix} A_1 & A_2\\A_2 & -A_1\end{matrix} \right)\) and relate the solvability of (\(*\)) to the matrix equation \(A_\sigma Y - Y B_\sigma = C _\sigma \in C^{2n,2n}\) having a real matrix solution (Theorem 1). This is extended and in turn classifies the coneigenvalues and coneigenvectors of \(A = SS^*\). Finally, a method for finding the coneigenvalues/coneigenvectors in this way is explained.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 6107739
zbMATH Keywords: Kennaugh's pseudo-eigenvalue equation
zbMATH Keywords: coneigenvalues
zbMATH Keywords: algorithm
zbMATH Keywords: radar polarimetry
zbMATH Keywords: Gaussian normal equations
zbMATH Keywords: matrix equation
zbMATH Keywords: coneigenvectors
MaRDI profile type: Publication
full work available at URL: s11464-011-0166-1
OpenAlex ID: W2067679033
cites work: The Matrix Equation $A\bar X - XB = C$ and Its Special Cases
cites work: A canonical form for matrices under consimilarity
cites work: Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix
cites work: On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)
DOI: 10.1007/S11464-011-0166-1
description: scientific article; zbMATH DE number 6107739