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| {{Unreferenced|date=November 2006}}
| | The writer's title is Christy Brookins. I've usually loved living in Mississippi. To perform domino is something I truly enjoy performing. Invoicing is what I do for a residing but I've usually wanted my own company.<br><br>Feel free to visit my web-site - clairvoyant psychic, [http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 cpacs.org], |
| In [[mathematics]], a '''signature matrix''' is a [[diagonal matrix]] whose diagonal elements are plus or minus 1, that is, any matrix of the form:
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| :<math>A=\begin{pmatrix}
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| \pm 1 & 0 & \cdots & 0 & 0 \\
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| 0 & \pm 1 & \cdots & 0 & 0 \\
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| \vdots & \vdots & \ddots & \vdots & \vdots \\
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| 0 & 0 & \cdots & \pm 1 & 0 \\
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| 0 & 0 & \cdots & 0 & \pm 1
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| \end{pmatrix}</math>
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| Any such matrix is its own [[inverse matrix|inverse]], hence is an [[involutary matrix]]. It is consequently a [[square root of a matrix|square root]] of the [[identity matrix]]. Note however that not all square roots of the identity are signature matrices.
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| Noting that signature matrices are both [[symmetric matrix|symmetric]] and involutary, they are thus [[orthogonal matrix|orthogonal]]. Consequently, any linear transformation corresponding to a signature matrix constitutes an [[isometry]].
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| Geometrically, signature matrices represent a [[reflection (mathematics)|reflection]] in each of the axes corresponding to the negated rows or columns.
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| ==See also==
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| * [[Involution (mathematics)]]
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| * [[Metric signature]]
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| {{DEFAULTSORT:Signature Matrix}}
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| [[Category:Matrices]]
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| {{Linear-algebra-stub}}
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Latest revision as of 13:02, 24 May 2014
The writer's title is Christy Brookins. I've usually loved living in Mississippi. To perform domino is something I truly enjoy performing. Invoicing is what I do for a residing but I've usually wanted my own company.
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