If we define the equivalence relation ~ for matrices $A$ and $B$ such that $A$~$B$ iff $A$ is row equivalent to $B$, then how many equivalence classes does this impose on the set of all matrices? More specifically, what is the cardinality of the set of all equivalence classes? Does the cardinality change if we only look at matrices of a certain size? Has this problem already been solved?
2026-03-31 17:54:20.1774979660
How many distinct matrices are there of a given size, up to row equivalence?
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