Class of finite-dimensional matrices with diagonals that majorize their spectrum
We define a special class of finite-dimensional matrices for which the diagonal majorizes the spectrum. This is the first class of matrices known to have this property, although the reverse majorization (i.e., the spectrum majorizing the diagonal) was previously known to hold for unitarily diagonali...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-02-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2022-0185 |
| _version_ | 1811159218355437568 |
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| author | Uhlmann Jeffrey |
| author_facet | Uhlmann Jeffrey |
| author_sort | Uhlmann Jeffrey |
| collection | DOAJ |
| description | We define a special class of finite-dimensional matrices for which the diagonal majorizes the spectrum. This is the first class of matrices known to have this property, although the reverse majorization (i.e., the spectrum majorizing the diagonal) was previously known to hold for unitarily diagonalizable (i.e., normal) matrices. Currently, these are the only known matrix classes that structurally provide a majorization relationship between their spectrum and diagonal. |
| first_indexed | 2024-04-10T05:37:22Z |
| format | Article |
| id | doaj.art-085bbc144a9f43859826eddf4752b076 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-04-10T05:37:22Z |
| publishDate | 2023-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-085bbc144a9f43859826eddf4752b0762023-03-06T16:56:41ZengDe GruyterSpecial Matrices2300-74512023-02-0111104200111710.1515/spma-2022-0185Class of finite-dimensional matrices with diagonals that majorize their spectrumUhlmann Jeffrey0Department of Electrical Engineering and Computer Science, University of Missouri-Columbia, 201 Naka Hall, Columbia, MO 65211, United StatesWe define a special class of finite-dimensional matrices for which the diagonal majorizes the spectrum. This is the first class of matrices known to have this property, although the reverse majorization (i.e., the spectrum majorizing the diagonal) was previously known to hold for unitarily diagonalizable (i.e., normal) matrices. Currently, these are the only known matrix classes that structurally provide a majorization relationship between their spectrum and diagonal.https://doi.org/10.1515/spma-2022-0185inverse relative gain arraypd diagonalizablepd-irga, majorizationpositive-definite similarityspecial matrices15-0615a57 |
| spellingShingle | Uhlmann Jeffrey Class of finite-dimensional matrices with diagonals that majorize their spectrum Special Matrices inverse relative gain array pd diagonalizable pd-irga, majorization positive-definite similarity special matrices 15-06 15a57 |
| title | Class of finite-dimensional matrices with diagonals that majorize their spectrum |
| title_full | Class of finite-dimensional matrices with diagonals that majorize their spectrum |
| title_fullStr | Class of finite-dimensional matrices with diagonals that majorize their spectrum |
| title_full_unstemmed | Class of finite-dimensional matrices with diagonals that majorize their spectrum |
| title_short | Class of finite-dimensional matrices with diagonals that majorize their spectrum |
| title_sort | class of finite dimensional matrices with diagonals that majorize their spectrum |
| topic | inverse relative gain array pd diagonalizable pd-irga, majorization positive-definite similarity special matrices 15-06 15a57 |
| url | https://doi.org/10.1515/spma-2022-0185 |
| work_keys_str_mv | AT uhlmannjeffrey classoffinitedimensionalmatriceswithdiagonalsthatmajorizetheirspectrum |