Flip a spreadsheet on its diagonal — rows become columns, columns become rows — and you've transposed a matrix. The transpose of [[1, 2, 3], [4, 5, 6]] is [[1, 4], [2, 5], [3, 6]]: the first row becomes the first column, so a 2×3 matrix becomes a 3×2. That shape swap is the whole operation, denoted Aᵀ, and it's deceptively powerful: symmetric matrices (equal to their own transpose) describe everything from covariance in statistics to the stiffness of a bridge, and the transpose is half of every "normal equation" in data science.

The rules are tidy: (Aᵀ)ᵀ = A (flipping twice restores the original), (A + B)ᵀ = Aᵀ + Bᵀ, and the famous reversal (AB)ᵀ = BᵀAᵀ — the order flips, the way putting on socks then shoes reverses when you undress. Students meet the transpose right before inverses and determinants, and it's the operation that makes row vectors and column vectors interchangeable. This calculator performs the transpose on your matrix values: enter them and read the flipped result. The one-second check: the entry that was in row 2, column 3 must now sit in row 3, column 2 — if the diagonal entries (1, 5) didn't stay put, something went wrong.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Transpose Matrix Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.