| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| 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,
|
