Talk:Linear
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The linearity of the function f(x)=mx+c over the reals is controversial.
- Let's get a closer look: all entities in Reals; just c may be 0...
- Superposition is not always satisfied:
- f(y+z)=m(y+z)+c is equal to f(y)+f(z)=my+c+mz+c=m(y+z)+2c iff c=0.
- Homogeneity is not always satisfied:
- af(x)=a(mx+c)=amx+ac is equal to f(ax)=amx+c iff c=0.
jimmer_lactic
- I've added that that's a different usage of the term linear. I hope that helps! -- Oliver P. 22:02 5 Jun 2003 (UTC)
Not true for all finite fields that superposition imples linearity: just for the prime fields.
Charles Matthews 06:37, 10 Oct 2003 (UTC)