The definition of "linearly independent" for a number of functions, say, , , ..., , is that for all possible values of the variables, regardless of how many variables there are, only if .
We know the definition of linearly independent of functions with one variable, and we know that the Wronskian is used to check the linearly independent.
But what is about the multivariable function? what is the definition of the linearly dependent of multivariable functions? Are there a Wronskian determinant for the multivariable functions.
Too late to edit my last post on this thread but I just noticed in my comment that quote was from Wikipedia , not HallsofIvy. I used "reply with quote" button under Ivy's comment but forgot to remove his user name from it so it looks a bit odd...