I am taking a course in linear algebra and I am having some trouble understanding the norm of error and the residual error. Our teacher define the norm of error as $$e=||\tilde X -x|| $$ And he defined the residual error as $$||A\tilde X - B||$$ I am just wondering how do I know when these numbers represent an ill conditioned system. When is the residual error and the norm of error too high? And do these error tell us if the system is ill conditioned or should we look at the conditioning number. I looked on the website but I couldn't find any material on this.
2026-03-25 11:27:18.1774438038
How to tell when residual error, and norm of eror is to small in Linear algebra
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