Importance of Matrix Transpose?

[EE-20]

what is the importance of matrix transpose?
what does it mean in the field of engineering specially signal processing 7 Communication?
does it physically explain any phenomenon?

 

[m_pourfathi]

Transpose in matrices is not realized as a physical phenomena. Matrices can be a mathematical description of something physical like an image or maybe the temperature of a room in different areas of the room. What transposing do is simply changing the rows and colomns in the matrix. It is a useful operator as it can change the dimension of the matrix. for example it can change a 2x3 matrix to a 3x2 matrix.
In DSP it sometimes can be used to change a set of algebra equations to a simple matrix equation which will make it easier to handle in simulation tools like MATLAB.
It is a very important operator in mathematics. And I remind you again. It does not mean anything physically.