What is the time complexity of quadratic probing and double hashing in the hash table?
I think it's pretty clear that if we have $ f (x) $ = $ x ^ 2 $ , then the function is defined positive, as for each value other than 0, $ x ^ 2 $ assumes a positive value. However, if I have
$ f (x, y, z, t) $ = $ x ^ 2 $ , is it always positive defined or is it only positive? Because if I calculate the associated matrix, I have three eigenvalues = 0, and the manual says that a matrix is definitely positive only if all its eigenvalues are positive. But what is the difference? According to the definition, a function is definitely positive if, regardless of the input outside of 0, the output is positive. Isn't that always the case?