It is well-known that the reduced row echelon form for a finite matrix is unique. I am wondering when such a result can be extended to an infinite matrix. Say I have an infinite matrix $A$ in row echelon form already, so that I can eliminate all nonzero entries above each pivot within a given column in a finite amount of steps (using Gaussian elimination). Will the resulting matrix be unique?
2026-03-25 04:38:55.1774413535
reduced row echelon form for an infinite matrix
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