Transpose

The transpose of a matrix is like rotating your data 90 degrees. Rows become columns, and columns become rows. Whether you’re prepping for matrix multiplication, defining symmetry, or just reshaping data for analysis, transposes are your go-to tool. 🔁

Transpose

The transpose of a matrix is formed by flipping it over its diagonal — turning row i into column i.

If A is an m \times n matrix, then its transpose A^\top (or sometimes A^T) is an n \times m matrix.

A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}

A^\top = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}

Transposes help define symmetry. A matrix A is symmetric if A = A^\top.