Matrix Transpose Calculator
Compute the transpose of any matrix. The transpose of an m×n matrix is an n×m matrix with rows and columns swapped.
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Notes
What is the Transpose?
The transpose of matrix A is written A^T. It is formed by swapping the row and column index of every element. A 2×3 matrix becomes a 3×2 matrix.
Example: 2×3 → 3×2
Original A (2×3):
| 1 | 2 | 3 |
| 4 | 5 | 6 |
A^T (3×2):
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |
A symmetric matrix satisfies A = A^T. Key identity: (AB)^T = B^T A^T — note the reversed order.
See also
- Matrix Calculations Guide — Matrix Transpose — In-depth notes on Matrix Transpose with worked examples
Frequently Asked Questions
What is the transpose of the transpose?
(A^T)^T = A — transposing twice returns the original matrix.
What is a symmetric matrix?
A matrix A is symmetric if A = A^T, meaning A[i][j] = A[j][i] for all i, j. Symmetric matrices must be square.
How does the transpose interact with matrix multiplication?
(AB)^T = B^T A^T — the transpose reverses the order of multiplication. This is a frequently used identity.