Abstract
In this paper, we prove some new norm inequalities for product of matrices. Among other results, we prove that if A and B are n \(\times \) n complex matrices, then
In particular, if \(\left| \left| \left| \cdot \right| \right| \right| =\left\| \cdot \right\| ,\) then
which is known as the Cauchy–Schwarz inequality. Also, we prove that if A and B are n \(\times \) n complex matrices, then
which is a refinement of the above Cauchy–Schwarz inequality. Here \( \left| \left| \left| \cdot \right| \right| \right| ,\) \(\left\| \cdot \right\| ,\) and \(w(\cdot )\) denote any unitarily invariant norm, the spectral norm, and the numerical radius of matrices, respectively.
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Al-Natoor, A. Norm inequalities for product of matrices. Acta Sci. Math. (Szeged) (2024). https://doi.org/10.1007/s44146-024-00121-1
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DOI: https://doi.org/10.1007/s44146-024-00121-1