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symmetric matrix
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(Definition)
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Definition:
Let $A=(a_{ij})$ be a square matrix of order $n$ The matrix $A$ is symmetric if $a_{ij} = a_{ji}$ for all $1 \leq i \leq n, 1 \leq j \leq n$
$A = \begin{pmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{n1} & \cdots & a_{nn} \end{pmatrix}$
Properties:
- $A^t = A$ where $A^t$ is the matrix transpose
Examples:
- $\begin{pmatrix} a & b \\ b & c \end{pmatrix}$
- $\begin{pmatrix} a & b & c \\ b & d & e \\ c & e & f \end{pmatrix}$
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"symmetric matrix" is owned by Daume.
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Cross-references: transpose, matrix, order, square matrix
There are 43 references to this entry.
This is version 9 of symmetric matrix, born on 2001-11-20, modified 2006-09-20.
Object id is 974, canonical name is SymmetricMatrix.
Accessed 22052 times total.
Classification:
| AMS MSC: | 15-00 (Linear and multilinear algebra; matrix theory :: General reference works ) |
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Pending Errata and Addenda
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