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ProductLogMajorization

Abstract

Horn weak log-majorization.

For arbitrary square complex matrices, each initial product of decreasing singular values of the product is at most the corresponding initial product for the two factors. Apply the largest-singular-value bound to their kth compound matrices.

The source is Alex Meiburg’s Apache-2.0 Physlib at revision b9043cc548ef6d63a28454cf3a57fb12a0c2e142. These results support the Schatten product Holder inequality. No mathematical originality is claimed.

References