- #1
Benn
- 34
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In my linear algebra course, we just finished proving the cayley hamilton theorem (if p(x) = det (A - xI), then p(A) = 0).
The theorem seems obvious: if you plug in A into p, you get det (A-AI) = det (0) = 0. But, of course, you can't do that (this is especially clear when you consider what A-xI looks like... you can't subtract matrices from real numbers)
Is there any way to salvage the idea of just plugging in A? or is it just a coincidence that it seems so obvious?
The theorem seems obvious: if you plug in A into p, you get det (A-AI) = det (0) = 0. But, of course, you can't do that (this is especially clear when you consider what A-xI looks like... you can't subtract matrices from real numbers)
Is there any way to salvage the idea of just plugging in A? or is it just a coincidence that it seems so obvious?