# Verifying the Transpose of a Linear Operator

I have a linear operator $\Phi$ in $\mathbb{R}^n$ and have created another operator that I believe to be its adjoint (transpose) $\Phi^T$.

What is the most direct way to verify that my $\Phi^T$ is indeed correct without having access to the matrix representation of $\Phi$ or $\Phi^T$?

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Compute $(\Phi x, y)$ and $(x, \Phi^T y)$, they should be the same.