A question about multivariable functions. How do we know if a multivariable function(or transform) is invertible? I mean just like we know y=2x is reversible and has an invert but y=x^2 is not invertible. What about multivariable functions? I've already known that we can determine if a matrix is reversible according to its determinant, but what about a nonlinear transform, and is it has anything to do with Jacobian matrix? Thanks!
2026-03-26 09:25:29.1774517129
How do we know if a multivariable function is invertible?
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The word you are looking for is "invertible." There is a relationship between invertibility and the Jacobian, and it is the inverse function theorem.