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In the HHL algorithm, they are solving a linear system $Ax=b$. This is achieved by embedding $A$ into a Hermitian matrix such as $$ H=\left(\begin{array}{cc} 0 & A \\ A^\dagger & 0 \end{array}\right). $$ If $A$ has singular values $\lambda$, then $H$ has eigenvalues $\pm\lambda$. So to all intents and purposes, they are the same thing in this context....

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