Matrix Transpose Calculator
Transpose any matrix by swapping its rows and columns to produce Aᵀ in a single step.
How does this calculator work?
The transpose Aᵀ flips a matrix over its main diagonal, turning each row into a column using Aᵀ[j][i] = A[i][j]. An m×n matrix becomes n×m while keeping all the same values. Enter your rows of numbers and the calculator returns Aᵀ along with its dimensions instantly.
Formula
How this is calculated
Enter matrix A as plain text, one row per line, with the numbers in each row separated by spaces or commas. The calculator parses this into an m×n array, where m is the number of rows and n is the number of columns. Every row must contain the same number of entries, and each entry must be a real number; otherwise the input is rejected.
The transpose Aᵀ is built by the rule Aᵀ[j][i] = A[i][j]. In words, the first row of A becomes the first column of Aᵀ, the second row becomes the second column, and so on. As a result an m×n matrix always transposes to an n×m matrix, so the dimensions swap.
Transposing is its own inverse: (Aᵀ)ᵀ = A. A square matrix keeps the same size, and a symmetric matrix equals its own transpose. The operation does not change any of the values, only their positions, so it works for integers, decimals, and negative numbers alike.
Frequently asked questions
It reflects the matrix across its main diagonal, turning each row into a column. The entry in row i, column j of A moves to row j, column i of Aᵀ.
If A is m×n (m rows, n columns), then Aᵀ is n×m. The row and column counts simply swap.
No. Transposing only rearranges the existing entries; their values are unchanged. Applying the transpose twice returns the original matrix.
Also known as
TG we-Calculate Editorial Team. (2026). Matrix Transpose Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/matrix-transpose-calculator
TG we-Calculate Editorial Team. "Matrix Transpose Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/matrix-transpose-calculator.
TG we-Calculate Editorial Team, "Matrix Transpose Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/matrix-transpose-calculator
@misc{wecalculate_matrix_transpose_calculator, title = {Matrix Transpose Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/matrix-transpose-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?