Skew-symmetric matrix

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric^[1]) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition^[2]^{: p. 38}

$A{\text{ skew-symmetric}}\quad \iff \quad A^{\textsf {T}}=-A.$

In terms of the entries of the matrix, if ${\textstyle a_{ij}}$ denotes the entry in the ${\textstyle i}$ -th row and ${\textstyle j}$ -th column, then the skew-symmetric condition is equivalent to

$A{\text{ skew-symmetric}}\quad \iff \quad a_{ji}=-a_{ij}.$

^ Richard A. Reyment; K. G. Jöreskog; Leslie F. Marcus (1996). Applied Factor Analysis in the Natural Sciences. Cambridge University Press. p. 68. ISBN 0-521-57556-7.
^ Lipschutz, Seymour; Lipson, Marc (September 2005). Schaum's Outline of Theory and Problems of Linear Algebra. McGraw-Hill. ISBN 9780070605022.

[1] Richard A. Reyment; K. G. Jöreskog; Leslie F. Marcus (1996). Applied Factor Analysis in the Natural Sciences. Cambridge University Press. p. 68. ISBN 0-521-57556-7.

[LipschutzLipson-2] Lipschutz, Seymour; Lipson, Marc (September 2005). Schaum's Outline of Theory and Problems of Linear Algebra. McGraw-Hill. ISBN 9780070605022.

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