Two non-zero vectors \(x\) and \(y\) are perpendicular if their dot product is zero. The dot product of two vectors \(x\) and \(y\) is denoted as \(x^Ty\). Therefore, the condition for \(x\) and \(y\) to be perpendicular is:
\[x^Ty = 0\]
So, the correct option is:
(A) \(x^Ty = 0\)