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Displaying similar documents to “A simple proof of the geometric-arithmetic mean inequality.”

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Necessary and sufficient conditions are presented for the commutativity equalities $A^{*} A^{D} = A^{D} A^{*}$ , $A^{†} A^{D} = A^{D} A^{†}$ , $A^{†} A A^{D} = A^{D} A A^{†}$ , $A A^{D} A^{*} = A^{*} A^{D} A$ and so on to hold by using rank equalities of matrices. Some related topics are also examined.