Editing Skew-symmetric matrix (section)

{{Short description|Form of a matrix}}
{{For|matrices with antisymmetry over the complex number field|Skew-Hermitian matrix}}
{{More footnotes|date=November 2009}}

In [[mathematics]], particularly in [[linear algebra]], a '''skew-symmetric''' (or '''antisymmetric''' or '''antimetric'''<ref>{{cite book |title=Applied Factor Analysis in the Natural Sciences | publisher=Cambridge University Press | year= 1996 | isbn=0-521-57556-7 | page=68 |author1 = Richard A. Reyment |author2 = K. G. Jöreskog |author3=Leslie F. Marcus | author-link2=K. G. Jöreskog }}</ref>) '''matrix''' is a [[square matrix]] whose [[transpose]] equals its negative. That is, it satisfies the condition<ref>{{cite book |title=Schaum's Outline of Theory and Problems of Linear Algebra |first1=Seymour |last1=Lipschutz |first2=Marc |last2=Lipson |date=September 2005 |isbn=9780070605022 |publisher=McGraw-Hill | page = 38}}</ref>

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|equation = <math>A \text{ skew-symmetric} \quad \iff \quad A^\textsf{T} = -A.</math>
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In terms of the entries of the matrix, if <math display="inline">a_{ij}</math> denotes the entry in the <math display="inline">i</math>-th row and <math display="inline">j</math>-th column, then the skew-symmetric condition is equivalent to

{{Equation box 1
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|equation = <math>A \text{ skew-symmetric} \quad \iff \quad a_{ij} = -a_{ji}.</math>
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