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Transposed Matrix

Transposed Matrix The transpose of a given matrix M of order mn is the matrix MT, which is obtained by exchanging the order of the indices: (mrs )T = (msr ). This new matrix MT 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 MTT equals M, where MTT is the transpose of the transpose of M.
Symmetric Matrix The matrix M is called symmetric if M = MT.
Skew-Symmetric Matrix If M = -MT, the matrix is called skew-symmetric or anti-symmetric.

Last Update: 2005-Jšn-25