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#### Keywords

Unitarily invariant norms, the Frobenius norm, Singular values

#### Abstract

Let $A$ and $B$ be complex square matrices. Some inequalities between $\mid A \mid + \mid B \mid$ and $\mid A^{*} \mid + \mid B^{*} \mid$ are established. Applications of these inequalities are also given. For example, in the Frobenius norm, $$\parallel\, A+B \,\parallel_{F} \leq \sqrt[4]{2} \parallel \mid A\mid + \mid B\mid \, \parallel_{F}.$$

abs_vol34_561-565.pdf (125 kB)
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