- #1
pellman
- 684
- 5
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.