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It is shown among other inequalities that if A, B and X are $$n\times n$$ complex matrices such that A and B are positive semidefinite, then $$s_{j}(AX-XB)\le $$ $$s_{j}\left( \left( \frac{1}{2}A+\frac{1}{2}A^{1/2}\left|… Click to show full abstract
It is shown among other inequalities that if A, B and X are $$n\times n$$ complex matrices such that A and B are positive semidefinite, then $$s_{j}(AX-XB)\le $$ $$s_{j}\left( \left( \frac{1}{2}A+\frac{1}{2}A^{1/2}\left| X^{*}\right| ^{2}A^{1/2}\right) \oplus \left( \frac{1}{2}B+\frac{1}{2} B^{1/2}\left| X\right| ^{2}B^{1/2}\right) \right) $$ for $$j=1,2,\ldots ,2n$$ . Several related singular value inequalities and norm inequalities are also given.
Keywords:
singular value;
inequalities applications;
right right;
value inequalities;
frac
Journal Title: Positivity
Year Published: 2020
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Journal Title: Positivity
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!