I am writing about a matrix (created on a spreadsheet) where inputing or changing element $\displaystyle a_{i,j}$ causes $\displaystyle (a_{i,j})^{-1}$ to appear at $\displaystyle a_{j,i}$. I am searching for the proper term for element $\displaystyle a_{j,i}$ relative to $\displaystyle a_{i,j}$.

Is it correct to refer to $\displaystyle a_{j,i}$ as thetransposeof $\displaystyle a_{i,j}$ (and vice versa)? I am only familiar with 'transpose' referring to whole matrices. Thank you very much.