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I have been trying to find an intuition for the transpose of a matrix. I have also read the posts in mathstackexhange but unfortunately it couldn’t help me.Can anyone please explain what is the idea behind the transpose of a matrix specially in linear algebra and operator theory? Thanks for consideration.

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    $\begingroup$ It is the matrix for the linear map on the dual spaces, equipped with the dual bases. Didn't you see that somewhere? $\endgroup$ – Bernard Feb 22 at 20:57
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    $\begingroup$ This question here and its answers gives a geometric interpretation of the transpose: math.stackexchange.com/questions/37398/… $\endgroup$ – Gregory Nisbet Feb 22 at 20:58
  • $\begingroup$ You can arrange $n$-tuples of numbers either as row or column vectors, and we take $m$ of them. $\endgroup$ – Berci Feb 22 at 20:59

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