Question

What is a matrix transpose?

Answer 1

The transpose of a matrix is found by creating new matrix where the rows and columns are swapped out. If i denotes row and j denotes column, we have `a_(ij)` becomes `a_(ji)`.

Suppose you have a matrix A. The transpose is denoted `A^T`. Let us take a 2 x 2 matrix for simplicity.

`a_(11)` is row 1, column 1. The transposed entry would stay the in the same place.

`a_(12)` is row 1, column 2. The transposed entry would be placed in Row 2, Column 1`a_(21)`.

`a_(21)` is row 2, column 1. The transposed entry would be placed in Row 1, Column 2`a_(12)`.

`a_(22)` is row 2, column 2. The transposed entry would stay in the same place.

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