Let A, B, and X be complex matrices of order n. We establish several novel singular value and norm inequalities, including: \(\begin{aligned} & \mu _{k}(\Re (AX^{*}B^{*}))\le \sqrt{\mu _{k}(A|X|A^{*}\oplus A|X|A^{*})\,\Vert B|X^{*}|B^{*}\Vert }\le \Vert X\Vert \Vert B\Vert \mu _{k}(A\oplus A), \\ & \quad \mu _{k}(AB^{*}+BA^{*})\le \mu _{k}((A^{*}A+B^{*}B)\oplus (AA^{*}+BB^{*})), \end{aligned}\) and for positive semidefinite matrices A and B, \(\begin{aligned} \mu _{k}(AX-YB)\le \max \{\Vert A\Vert ,\Vert B\Vert \}\left( \frac{\mu _{k}((X-Y)\oplus (X-Y))}{2}+\max \{\Vert X\Vert ,\Vert Y\Vert \}\right) . \end{aligned}\) The first and second inequalities establish variants of well-known singular value inequalities, while the third result generalizes a commutator inequality for positive semidefinite matrices previously established by Kittaneh. Additionally, we extend several classical singular value inequalities to functional settings, broadening their scope and applicability.
