Symmetric matrix: Difference between revisions

Revision as of 06:01, 17 March 2021

Revision as of 20:45, 17 March 2021

Line 1:

{{Use American English|date=January 2019}}{{Short description|Matrix equal to its transpose

}}

{{forFor|matrices with symmetry over the [[complex number]] field|Hermitian matrix}}

{{Use American English|date=January 2019}}

[[File:Matrix symmetry qtl1.svg|thumb|Symmetry of a 5×5 matrix]]

Line 48:

===Basic properties===

* The sum and difference of two symmetric matrices is again 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 integer <math>n</math>, <math>A^n</math> is symmetric if <math>A</math> is symmetric.

* For 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.

Line 162 ⟶ 159:

* [https://fylux.github.io/2017/03/07/Symmetric-Triangular-Matrix/ How to implement a Symmetric Matrix in C++]

{{Matrix classes}}

{{Authority control}}

[[Category:Matrices]]