Transpositions matrix

In the context of linear algebra and matrix theory, a transposition matrix typically refers to a permutation matrix that swaps two rows or two columns of an identity matrix. ### Definition 1. **Permutation Matrix**: A permutation matrix is a square matrix obtained by permuting the rows (or columns) of an identity matrix. 2. **Transposition**: Specifically, a transposition involves swapping two elements, so a transposition matrix will swap the corresponding rows or columns in the identity matrix.