Abstract
In this paper, we give refinements for the G-majorization triangle inequality with vectors of an Eaton triple and normal map . For instance, we establish refinements for the majorization Ky Fan's eigenvalue inequality with Hermitian matrices x and y and the eigenvalue operator . Likewise, we show refinements for the weak majorization Ky Fan's singular value inequality with complex matrices x and y, where stands for the singular values operator. In particular, we recover original Maligranda's refinement of the norm triangle inequality.
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