Correctness of a mathematical algorithm is of course defined by whether it meets a mathematical definition. In this case, correctness of matrix multiplication

Correctness of a mathematical algorithm is of course defined by whether it meets a mathematical definition. In this case, correctness of matrix multiplication is only defined by whether it meets the mathematical definition of matrix multiplication. That's it. That's the whole thing. Correctness of all computer science algorithms is defined by whether they meet a particular algorithmic specification. That's literally the definition of correctness: https://en.wikipedia.org/wiki/Correctness_(computer_science) https://en.wikipedia.org/wiki/Correctness_(computer_science) "In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified" The specification is the matrix multiplication definition given right on that Wikipedia page. this algorithm meets it. It is therefore correct. (again, "error" does not appear on the page here either). There is no separate, special definition for "correctness (mathematical)" or "correctness (eigenket)". You really seem to want to there to be one, but it ain't there. You really really really don't want to let this go, but the problem is - nothing, anywhere, agrees with you that correctness and usefulness are the same thing. Nor can you cite any reference, like i just did, to correctness that requires it do anything other than meet the specified mathematical definition. Your papers don't do it, my books don't do it. Nothing does it. Because it's not a thing. My college textbooks talk about error analysis. I did not claim otherwise. They talk about it in the context of how to make an algorithm useful for a particular purpose, not about correctness. They are not making a ridiculous claim like you are. I'm not going down this path anymore with you. Believe what you want, the rest of us will continue to not confuse it, and sources that people look at (textbooks, wikipedia, etc) will continue to not lead them astray. I can only hope that at some point, you too stop trying to do so.