Convert OnlineConvertOnline

Matrix TransposeCalculator

Matrix A size: x





Answer




How to use this Matrix Transpose Calculator 🤔

Follow these steps to perform Matrix Transpose for the given matrices.

  1. Enter the matrix size for matrix A.
  2. Based on the given matrix size, a matrix of input fields appears. Enter the matrix elements.
  3. As and when you complete entering the matrix elements, Matrix Transpose is calculated, and displayed in the answer section.

Matrix Transpose

The transpose of a matrix is obtained by swapping the rows and columns. If A is a matrix with dimensions m x n, then the transpose of A, denoted as AT, is an n x m matrix where the rows of A become the columns of AT and the columns of A become the rows of AT.

Given a matrix A, the transpose AT is computed as:


A^T[i][j] = A[j][i]

where 1 ≤ i ≤ n and 1 ≤ j ≤ m.

Example 1

Let's transpose the following matrix:

\( A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \)

The transpose of A is:

\( A^T = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix} \)

Example 2

Consider another example with a different matrix:

\( A = \begin{bmatrix} 2 & 4 \\ 6 & 8 \\ 10 & 12 \end{bmatrix} \)

The transpose of A is:

\( A^T = \begin{bmatrix} 2 & 6 & 10 \\ 4 & 8 & 12 \end{bmatrix} \)

These examples demonstrate the basic process of matrix transpose by swapping the rows and columns of the input matrices to get the resultant matrix.