What is a matrix transpose?

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What is a matrix transpose?

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Answer 1 · 2014-08-19T19:03:32

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 $a_{i j}$ $a_(ij)$ becomes $a_{j i}$ $a_(ji)$ .

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

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

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

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

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

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What is a matrix transpose?

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