1. The definition of A- unitary matrix and six main properties were given to popularize the concept of unitary matrix.

2. The properties of the unitary matrix for the localization of molecular orbitals were discussed.

3. A unitary matrix extension method of the corresponding vectors, obtained from multiple channel low-pass filters by polyphase factorization, is proposed.

4. The unitary matrix was constructed by using eigenstates of the controlled quantum system so as to perform a coordinate rotation on the controlled system.

5. The main results are as following:(1) The unitary matrix was constructed by using eigenstates of the controlled quantum system so as to perform a coordinate rotation on the controlled system.

6. This paper has popularized the concept of unitary matrix, introduced the column (row) unitary matrix and discussed their properties.

7. A lossless polarization transfer matrix is a unitary matrix(http://sentencedict.com), and reciprocal forward and backward polarization transfer matrices are transposed each other.

8. We introduce some important matrices and their applications in quantum computation and quantum information, including density matrix, unitary matrix, etc.

9. The key of this method is to spread a perfect sequence by correlation product of the shift sequences set of the perfect sequence and corresponding unitary matrix.

10. An approach of constructing bivariate orthogonal multi-wavelet function is presented by given bivariate orthogonal uni-wavelet function based on the unitary matrix.

11. In this paper, backward errors for seven kinds of structured unitary matrix eigenvalue problems are discussed.

12. T he concept of the subnormal matrix and anti-symmetric matrix is introduced, th eir basic properties and relations with the sub-symmetric matrix and the unitary matrix are studied.