Transpose a matrix — flip its rows and columns. Enter the matrix with rows separated by semicolons.
Usage Tip
A matrix equal to its own transpose is symmetric — common in covariance and distance matrices.
An m×n matrix becomes n×m
It is fundamental to dot products, symmetric matrices, and many linear-algebra identities.
The result has the dimensions swapped.
Transposing twice returns the original matrix.
The transpose of a matrix swaps its rows and columns, so the entry in row i and column j moves to row j and column i. A matrix with 2 rows and 3 columns becomes one with 3 rows and 2 columns, and a square matrix stays the same size.
Transposes appear in many matrix identities. The transpose of a product reverses the order, so the transpose of A times B equals the transpose of B times the transpose of A. A matrix equal to its own transpose is called symmetric, and one whose transpose equals its negative is called skew symmetric. The transpose is also used to convert between row vectors and column vectors.