|
|
| Line 1: |
Line 1: |
| {{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:
| |
| | |
| :<math>A=\begin{pmatrix}
| |
| \pm 1 & 0 & \cdots & 0 & 0 \\
| |
| 0 & \pm 1 & \cdots & 0 & 0 \\
| |
| \vdots & \vdots & \ddots & \vdots & \vdots \\
| |
| 0 & 0 & \cdots & \pm 1 & 0 \\
| |
| 0 & 0 & \cdots & 0 & \pm 1
| |
| \end{pmatrix}</math>
| |
| | |
| 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.
| |
| | |
| 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]].
| |
| | |
| Geometrically, signature matrices represent a [[reflection (mathematics)|reflection]] in each of the axes corresponding to the negated rows or columns.
| |
| | |
| ==See also==
| |
| * [[Involution (mathematics)]]
| |
| * [[Metric signature]]
| |
| | |
| {{DEFAULTSORT:Signature Matrix}}
| |
| [[Category:Matrices]]
| |
| | |
| | |
| {{Linear-algebra-stub}}
| |
Latest revision as of 12:02, 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.
Feel free to visit my web-site - clairvoyant psychic, cpacs.org,