Enter your matrix values and dimensions, then get the transposed matrix instantly. Set the number of rows and columns (up to 4×4), fill in the matrix elements, and the calculator flips rows into columns — showing you the full transpose result along with the matrix dimensions.
Transposed Matrix Dimensions
--
Original Matrix Dimensions
--
Matrix Type
--
Is Symmetric?
--
The transpose of a matrix is a new matrix formed by flipping the original over its main diagonal — every row becomes a column and every column becomes a row. If your original matrix has dimensions n × m, the transposed matrix will have dimensions m × n.
To transpose a matrix, take element at position [i][j] in the original and place it at position [j][i] in the new matrix. For example, the element in row 1, column 3 moves to row 3, column 1 in the transposed matrix.
Yes — the dimensions swap. A 2×3 matrix (2 rows, 3 columns) becomes a 3×2 matrix (3 rows, 2 columns) after transposition. The only exception is square matrices (n×n), which retain the same dimensions.
A matrix is symmetric if it equals its own transpose, meaning A = Aᵀ. This is only possible for square matrices where element [i][j] equals element [j][i] for all positions.
When you transpose a square matrix, the dimensions stay the same (n×n), but the off-diagonal elements are mirrored across the main diagonal. The diagonal elements themselves remain unchanged.
Transposing a matrix twice returns you to the original matrix. In mathematical notation, (Aᵀ)ᵀ = A. The double transpose is always equal to the starting matrix.
The transpose of a 1×n row matrix (a single row vector) is an n×1 column matrix (a column vector). Each element that was arranged horizontally is stacked vertically in the result.
Transposing matrices is fundamental in linear algebra, statistics, and machine learning. It is used in operations like computing dot products, solving systems of equations, performing PCA (principal component analysis), and working with covariance matrices.