Editing Symmetric matrix (section)

===Basic properties===
* The sum and difference of two symmetric matrices is symmetric.
* This is not always true for the [[matrix multiplication|product]]: given symmetric matrices <math>A</math> and <math>B</math>, then <math>AB</math> is symmetric if and only if <math>A</math> and <math>B</math> [[commutativity|commute]], i.e., if <math>AB=BA</math>.
* For any integer <math>n</math>, <math>A^n</math> is symmetric if <math>A</math> is symmetric.
* If <math>A^{-1}</math> exists, it is symmetric if and only if <math>A</math> is symmetric.
* Rank of a symmetric matrix <math>A</math> is equal to the number of non-zero eigenvalues of <math>A</math>.