Image Matrix Vector Representation for the Degradation Model
Indeed since both expressions are scalars then they are equal to each other since the transpose of a scalar is the same scalar.
See in MATLAB as an example (Calculating $ {x}^{T} H y $ and $ {y}^{T} {H}^{T} x $:
&gt;&gt; vX = randn(10, 1);
&gt;&gt; vY = randn(10, 1);
&gt;&gt; mH = randn(10, 10);
&gt;&gt; vX.' * mH.' * vY

ans = -0.8618

&gt;&gt; vY.' * mH * vX

ans = -0.8618


As you can see, indeed both expressions are scalars.
As expected $ {x}^{T} H y = {\left( {x}^{T} H y \right)}^{T} = {y}^{T} {H}^{T} x $.