In this paper, we establish several comparisons for the new spectral geometric mean Ft(A,B)=(A−1♯tB)1/2A2−2t(A−1♯tB)1/2 of two positive definite matrices A and B. We compare Ft(A,B) with three well-known matrix means: the arithmetic mean, the geometric mean, and the harmonic mean, considering two cases: t∈[0,1] and t∉[0,1].
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Vuong et al. (2026) studied this question.
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