ConvertOnlineMatrix TransposeCalculator
Matrix A size: x
Answer
How to use this Matrix Transpose Calculator 🤔
Follow these steps to perform Matrix Transpose for the given matrices.
- Enter the matrix size for matrix A.
- Based on the given matrix size, a matrix of input fields appears. Enter the matrix elements.
- 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.