释义 |
Symmetric MatrixA symmetric matrix is a Square Matrix which satisfies where denotes theTranspose, so . This also implies
 | (1) |
where I is the Identity Matrix. Written explicitly,
 | (2) |
The symmetric part of any Matrix may be obtained from
 | (3) |
A Matrix A is symmetric if it can be expressed in the form
 | (4) |
where is an Orthogonal Matrix and is a Diagonal Matrix. This is equivalent to theMatrix equation
 | (5) |
which is equivalent to
 | (6) |
for all , where . Therefore, the diagonal elements of are the Eigenvalues of , and the columns of are the corresponding Eigenvectors.See also Antisymmetric Matrix, Skew Symmetric Matrix References
Nash, J. C. ``Real Symmetric Matrices.'' Ch. 10 in Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol, England: Adam Hilger, pp. 119-134, 1990.
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