What properties do a pair of matrices have if they share same ordered right singular vectors? Or for a specical case the matrices are square, what properties do they have if their ordered eigen-vectors are the same? And only consider the singular (or eigen-) vectors, it is fine if their singular (or eigen-) values are different. I know simultaneously diagonalizable and commuting family may be a view to analyse this question when the matrices are square.
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The word you are looking for is spelled singular. – Gerry Myerson Mar 31 '20 at 09:35
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Thank you@GerryMyerson, I correct it. – user765703 Apr 01 '20 at 10:04
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You corrected it in the title, but left it in the body. – Gerry Myerson Apr 01 '20 at 12:26
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Never mind, I fixed it for you. – Gerry Myerson Apr 03 '20 at 11:48