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ntvy95 · #2 05-05-2016, 11:32 AM

Quote:

Originally Posted by pouramini

The book says

How a point in Z can be not a valid transform of any x?

I suppose any x will be mapped to a z! not!?

Here is my understanding:

Any

should be mapped to a

, but not any

can be mapped to a

: In other words, nonlinear transform $\Phi$ may not be an onto function.

For example the nonlinear transform $z = \Phi (x) = [1, x^{2}_{1}, x^{2}_{2}]$ (given in the book), if $z_{1} < 0$ or $z_{2} < 0$ then there is no

can be mapped to such

because there is no $x_{1}$ such that $z_{1} = x_{1}^{2} < 0$ and no $x_{2}$ such that $z_{2} = x_{2}^{2} < 0$ .

Hope this helps.