The main goal of this work is to present new matrix inequalities of Cauchy-Schwarz type.In particular, we investigate the so-called Lieb functions, whose definition came as an umbrella of Cauchy-Schwarz-like inequalities, then we consider the mixed Cauchy-Schwarz inequality.This latter inequality has been influential in obtaining several other matrix inequalities, including numerical radius and norm results.Among many other results, we show thatwhere RT is the real part of the matrix T .
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Sababheh et al. (2023) studied this question.
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