Antisymmetric Matrix Diagonal

As we know, an antisymmetric matrix $A$ satisfies the property $A^T = -A$. Let’s consider the diagonal elements of $A$ denoted by $a_{ii}$.

According to the definition of the transpose, the diagonal elements of $A^T$ are given by $a_{ii}^T = a_{ii}$. Since $A^T = -A$, we have $a_{ii} = -a_{ii}$.

Solving this equation, we find that $a_{ii} = 0$ for all $i$. Therefore, the diagonal elements of an antisymmetric matrix are zero.