Let W be a vector space and let A be a linear operator W --> W. Isn't it the case that for any such A, the kernel of A is the zero vector and the range is all of W? And that it is one-to-one from linearity? I ask because an author I am reading goes through a lot of steps to show that a certain operator is one-to-one and onto yet I thought it was a given for any linear operator.(adsbygoogle = window.adsbygoogle || []).push({});

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# I Aren't all linear operators one-to-one and onto?

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