- #1
Felipe_
- 3
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Hi!
Studying the introductory chapters of a Operator Theory book, I have found that the author seem to find a lot of demonstrations "easy" and not worthy of demonstrations. Yet, I don't have such ease as he has... For instance, one that has bugged me (on several books) is the proof that:
range(I-E)=nullspace(E)
nullspace(I-E)=range(E)
where E is a projection and I is the identity matrix.
It always follows stating that its is simple, then, to tell the set of all surjective projections of a linear transformation L.
How are they related? I can't seem to find any way to prove/answer the above and its been a couple of days now.
Can anyone shed some light in this? I'd really appreciate it!
Thanks!
Felipe
Studying the introductory chapters of a Operator Theory book, I have found that the author seem to find a lot of demonstrations "easy" and not worthy of demonstrations. Yet, I don't have such ease as he has... For instance, one that has bugged me (on several books) is the proof that:
range(I-E)=nullspace(E)
nullspace(I-E)=range(E)
where E is a projection and I is the identity matrix.
It always follows stating that its is simple, then, to tell the set of all surjective projections of a linear transformation L.
How are they related? I can't seem to find any way to prove/answer the above and its been a couple of days now.
Can anyone shed some light in this? I'd really appreciate it!
Thanks!
Felipe