Matrix Transpose
The transpose of a matrix A, written Aᵀ, swaps its rows and columns: the entry in row i and column j of Aᵀ equals the entry in row j and column i of A. Enter your matrix and the calculator returns Aᵀ.
Frequently asked questions
Does the matrix have to be square?
No. Any m×n matrix has a transpose, which is an n×m matrix.
What is the transpose of a transpose?
(Aᵀ)ᵀ = A. Transposing twice returns the original matrix.
When is a matrix symmetric?
When A = Aᵀ. This is only possible for square matrices, and corresponds to the entries being mirrored across the main diagonal.