2017 Fiscal Year Final Research Report
Algebraic curve theoretic study of numerical ranges of matrices and operators and its applications
| Project/Area Number |
15K04890
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hirosaki University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 正方行列 / 線形作用素 / 数域 / 代数曲線 / 特異点 / 重みつきシフト行列 / 縮小作用素 / テープリッツ行列 |
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| Outline of Final Research Achievements |
The numerical range of a matrix or a linear operator is a subset of the Gaussian plane which is invariant under unitary transformations. It is known that the numerical range is determined by the simultaneous characteristic polynomial of the Hermitian part and the skew Hermitian part of the matrix (or the operator). The inverse problem was posed about 50 years ago. The problem was affirmatively solved about 10 years ago by Czech and American mathematicians. But some related interesting problems were still open. In this subject, I solved some related problems. The problem is also related to the entanglement of the quantum physics. The discovered method provides a linear theoretic model to treat operators via numerical ranges. Especially some new properties of Toeplitz matrices and weighted cyclic shift matrices are found by this research. These results provide new aspects to study these special matrices,
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| Free Research Field |
数物系科学
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