symmetric matrices, Hermite matrices, orthogonal matrices, unitary matrices, singular matrices, normal matrices, idempotent matrices

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Title: symmetric matrix, Hermite matrix, orthogonal matrix, unitary matrix, singular matrix, normal matrix, idempotent matrix

Look at the literature, often see a variety of matrices, this chapter summarizes the common symmetry matrix, Hermite matrix, orthogonal matrix, unitary matrix, singular matrix, normal matrix, idempotent matrix seven kinds of matrix definitions, as a concept memo, forget can always check.

1. Symmetric matrix (document "1", page 40th)

where superscript t represents the transpose of the Matrix (document "1" 第38-39 page)

2. Hermite Matrix (document "2" on page 97th)

where h denotes a complex conjugate transpose of the Matrix: (document "2" on page 96th)

Hermite array is the generalization of the concept of symmetric array, the symmetric array is real matrix, and the Hermite array is for complex matrix.

3. Orthogonal matrix (document "1", page 115th)

4. Unitary Matrix (document "2" on page 102th)

The unitary matrix is a generalization of the concept of orthogonal array, which is similar to the Hermite array in relation to symmetric matrices.

5. Singular matrix (document "1", page 43rd)

6, the normal matrix (the document "2" the 119th page)

7, idempotent Matrix (document "2" 第106-107 page)

Reference documents:

"1" Mathematics Department of Tongji University. Linear algebra of Engineering Mathematics [M]. Version 5. Higher Education Press, 2007.

"2" Shrongchang, Wei Feng. Matrix analysis [M]. Version 3. Beijing: Beijing Polytechnic University Press, 2010.

symmetric matrices, Hermite matrices, orthogonal matrices, unitary matrices, singular matrices, normal matrices, idempotent matrices