PlanetMath: anti-diagonal matrix

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anti-diagonal matrix

(Definition)

Let be a square matrix (over any field $\mathbbmss{F}$ ). An entry in is an anti-diagonal entry if it is on the line going from the lower left corner of to the upper right corner. If all entries in are zero except on the anti-diagonal, then is an anti-diagonal matrix.

If $a_1, \ldots, a_n \in \mathbbmss{F}$ , let

$\displaystyle \operatorname{adiag}(a_1, \ldots, a_n) = \begin{pmatrix} 0 & 0 & ... ...& 0 & a_{3} & & 0 \ 0 & \cdot & 0 & & 0 \ a_n & 0 & 0 & & 0 \end{pmatrix}.$

Properties of anti-diagonal matrices

If and are $n\times n$ anti-diagonal and diagonal matrices, respectively, then are anti-diagonal.
The product of two anti-diagonal matrices is an diagonal matrix.

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"anti-diagonal matrix" is owned by matte. [ full author list (3) ]

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Attachments:: determinant of anti-diagonal matrix (Result) by cvalente

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Cross-references: product, diagonal matrices, right, line, field, square matrix
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This is version 5 of anti-diagonal matrix, born on 2005-04-24, modified 2006-06-12.
Object id is 6964, canonical name is AntiDiagonalMatrix.
Accessed 2159 times total.

Classification:

AMS MSC:

15-00 (Linear and multilinear algebra; matrix theory :: General reference works )

Pending Errata and Addenda

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