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On the phases of a ...
On the phases of a semi-sectorial matrix and the essential phase of a Laplacian
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- Wang, Dan (författare)
- KTH,Reglerteknik
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- Mao, Xin (författare)
- Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
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- Chen, Wei (författare)
- Department of Mechanics and Engineering Science & State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, China
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- Qiu, Li (författare)
- Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China, Clear Water Bay; Southern University of Science and Technology, Shenzhen, China
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(creator_code:org_t)
- Elsevier BV, 2023
- 2023
- Engelska.
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 676, s. 441-458
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- In this paper, we extend the definition of phases of sectorial matrices to those of semi-sectorial matrices, which are possibly singular. Properties of the phases are also extended, including those of the Moore-Penrose generalized inverse, compressions and Schur complements, matrix sums and products. In particular, an interlacing relation is established between the phases of A+B and those of A and B combined. Also, a majorization relation is established between the phases of the nonzero eigenvalues of AB and the phases of the compressions of A and B, which leads to a generalized matrix small phase theorem. For the matrices which are not necessarily semi-sectorial, we define their (largest and smallest) essential phases via diagonal similarity transformation. An explicit expression for the essential phases of a Laplacian matrix of a directed graph is obtained.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
Nyckelord
- Essential phase
- Laplacian
- Majorization
- Matrix small phase theorem
- Phase
- Semi-sectorial matrix
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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