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Transposed Matrix
Transposed Matrix 
The transpose of a given matrix M of order mn is
the matrix M^{T}, which is
obtained by exchanging the order of the indices: (m_{rs
})^{T} = (m_{sr }). This new
matrix M^{T} is of the order
nm. 
More simply expressed, we just write the rows as columns, and vice versa.
Here is an example:
It is evident that M^{TT} equals M, where
M^{TT} is the
transpose of the transpose of M.
Symmetric Matrix 
The matrix M is called symmetric if M
= M^{T}. 
SkewSymmetric Matrix 
If M = M^{T}, the matrix is called skewsymmetric or
antisymmetric. 
Last Update: 2005Jän25