Matrix Transpose Calculator
Calculate the transpose of any matrix by swapping rows and columns.
Matrix Dimensions
Original Matrix A (3x3)
Square Matrix Properties
Trace15.0000
Symmetric (A = A^T)No
Skew-Symmetric (A = -A^T)No
Transpose A^T (3x3)
1.00
4.00
7.00
2.00
5.00
8.00
3.00
6.00
9.00
How Transpose Works
(A^T)[i][j] = A[j][i]
The transpose switches rows and columns. Row i becomes column i.
Properties of Transpose
- (A^T)^T = A (double transpose equals original)
- (A + B)^T = A^T + B^T
- (kA)^T = k(A^T) for scalar k
- (AB)^T = B^T * A^T
- det(A^T) = det(A)
Applications
- Computing dot products: A^T * B
- Symmetric matrices in physics
- Machine learning weight matrices
- Graphics transformations