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X3 matrix A with elements a11, a12, a13, a21, a22, a23, a31, a32, and a33.
The transpose of matrix A, denoted as A^T, is obtained by interchanging the rows and columns of matrix A.
So, the transpose of matrix A can be written as:
A^T = [a11, a21, a31;
a12, a22, a32;
a13, a23, a33]
In other words, the element in the i-th row and j-th column of matrix A becomes the element in the j-th row and i-th column of matrix A^T.
For example, if A = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the transpose of A, denoted as A^T, would be:
A^T = [1, 4, 7; 2, 5, 8; 3, 6, 9]