Some results on matrix means

Let A, B and C be \(n\times n\) positive semi-definite matrices. We characterize \(C\le A ! B\), namely the harmonic mean of A, B, and apply it to show that if \(0

Keywords:

• Geometric mean
• Matrix (mathematics)
• Invertible matrix
• Real number
• Combinatorics
• Generalized inverse
• Physics
• Harmonic mean
• Operator theory
• Identity matrix

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