Toeplitz Matrices are Unitarily Similar to Symmetric Matrices
Type of DegreePhD Dissertation
DepartmentMathematics and Statistics
MetadataShow full item record
We prove that Toeplitz matrices are unitarily similar to complex symmetric matrices. Moreover, two $n\times n$ unitary matrices that uniformly turn all $n\times n$ Toeplitz matrices via similarity to complex symmetric matrices are explicitly given, respectively. When $n\leq 3$, we prove that each complex symmetric matrix is unitarily similar to some Toeplitz matrix, but the statement is false when n > 3.
- Toeplitz Matrices are Unitarily Similar to Symmetric Matrices.pdf