What Does Transposing a Matrix Do?

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A^T (among other notations).

What is the purpose of transposing a matrix?

- here the transpose of a matrix is used to obtain a system of equations that can be solved with the method of matrix inverses. The transpose of also plays an important role in estimating variances and covariances in regression.

Does transposing a matrix change anything?

Proof by induction that transposing a matrix does not change its determinant.