Editing Trace (linear algebra) (section)

== Definition ==
The '''trace''' of an {{math|''n'' × ''n''}} [[square matrix]] {{math|'''A'''}} is defined as<ref name=":1"/><ref name=":2">{{cite encyclopedia |title=Trace (matrix) |last1=Weisstein |first1=Eric W. |author1-link=Eric W. Weisstein |editor1-first=Eric W. |editor1-last=Weisstein |encyclopedia=[[CRC Concise Encyclopedia of Mathematics]] |edition=2nd |orig-date=1999 |year=2003 |publisher=[[Chapman & Hall]] |location=Boca Raton, FL |isbn=1-58488-347-2|mr=1944431 |url=https://mathworld.wolfram.com/MatrixTrace.html|access-date=2020-09-09|zbl=1079.00009|doi=10.1201/9781420035223|url-access=subscription }}
</ref><ref name=LipschutzLipson>{{cite book |first1=Seymour |last1=Lipschutz |first2=Marc |last2=Lipson |date=September 2005 |title=Theory and Problems of Linear Algebra |series=Schaum's Outline |publisher=McGraw-Hill |isbn=9780070605022 }}</ref>{{rp|34}}
<math display="block">\operatorname{tr}(\mathbf{A}) = \sum_{i=1}^n a_{ii} = a_{11} + a_{22} + \dots + a_{nn}</math>
where {{math|''a<sub>ii</sub>''}} denotes the entry on the {{nobr|{{mvar|i}}&thinsp;th}} row and {{nobr|{{mvar|i}}&thinsp;th}} column of {{math|'''A'''}}. The entries of {{math|'''A'''}} can be [[real number]]s, [[complex numbers]], or more generally elements of a [[field (mathematics)|field]] {{mvar|F}}. The trace is not defined for non-square matrices.