The DOI matches its Crossref record.
When Is A Linear Operator Diagonalizable?
Abstract
INTRODUCTION. As it often happens, everything began with a mistake. I was teaching for the third year in a row a linear algebra course to engineering freshmen. One of the highlights of the course was eigenvector theory, and in particular the diagonalization of linear operators on finite-dimensional vector spaces (i.e., of square real or complex matrices). Toward the end of the course I assigned a standard homework: prove that the matrix
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In the citing paper
“In addition, the fact that 〈 〈 ξ k | is orthogornal to | ζ k ′ 〉 〉 , (199), even though the two sets {〈 〈 ξ k | } and {| ζ k 〉 〉} are not conjugate transpose of each other, implies that the superoperators {| ζ k 〉 〉〈 〈 ξ k | } constitute what we call a biorthonormal basis [44, 45] for S d .”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [45]
In the citing paper
“The concept of biorthonormal basis [44, 45] plays an important role in non-Hermitian quantum mechanics.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [45]
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Fundamentals of quantum mechanics in Liouville space
Gyamfi, J. A. (2020) · European Journal of Physics · doi:10.1088/1361-6404/ab9fdd · Cited by 77
Metadata
- Authors
- Abate, M.
- Affiliations
- Dipartimento di Matematica Università di Ancona Via Brecce Bianche 60131 Ancona, Italy
- Corresponding author
- Abate, Marco
- ORCID
- Abate, Marco
- Venue
- The American Mathematical Monthly
- Publisher
- Informa UK Limited
- Published
- 1997-11
- Volume
- 104
- Issue
- 9
- Pages
- 824-830
- ISSN
- 0002-9890 (ISSN-L)
- 1930-0972
- OpenAlex
- W1991057939
- Cited by
- 10
- References
- 0
- Citations by year
- 2025: 1 · 2020: 2 · 2018: 1 · 2012: 1
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Mathematical Monthly (publishedVersion)
- CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Algebra and Number Theory › Rings, Modules, and Algebras
- Physical Sciences › Mathematics › Applied Mathematics › Holomorphic and Operator Theory
- Keywords
- diagonalizability, linear operators, eigenvectors, eigenvalues, finite-dimensional vector spaces, diagonalization, linear algebra education
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