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## Toeplitz Matrices are Unitarily Similar to Symmetric Matrices

##### Date

2017-07-25##### Author

Liu, Jianzhen

##### Type of Degree

PhD Dissertation##### Department

Mathematics and Statistics##### Metadata

Show full item record##### Abstract

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.

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- Toeplitz Matrices are Unitarily Similar to Symmetric Matrices.pdf
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