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The transpose of a matrix , denoted by , , , or , may be constructed by any of the following methods:
#Reflect over its main diagonal (which runs from the top left to the bottom right) to obtain
#Write the rows of as the columns of
#Write the columns of as the rows of

Formally, the th row, th column element of is the th row, th column element of :
:

If is an matrix, then is an matrix.

Matrix definitions involving transposition

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