Symmetric matrix: Difference between revisions

Revision as of 13:31, 5 August 2021

Revision as of 13:31, 5 August 2021

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== Properties ==

===Basic properties===

* The sum and difference of two symmetric matrices is again skewsymmetricsymmetric

* 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 integer <math>n</math>, <math>A^n</math> is symmetric if <math>A</math> is symmetric.