Replacement Theorem Proof
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- Опубліковано 8 вер 2024
- Proof of the replacement theorem, one of the most important theorems in linear algebra. It intuitively says that any linearly independent set can be extended to be a spanning set. It is used, for example, to show that the notion of dimension is well-defined. The proof is absolutely beautiful and requires use of the intruder theorem. Enjoy!
Replacement Theorem Video: • Replacement Theorem
Intruder Theorem Video: • Intruder Theorem
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Como siempre...fantástico. Gracias Dr. Peyam.
Thank you so much for making this video online linear algebra is rough.
he is so happy *and* he has "Dr" that is not allowed
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Correct me if I missed it, but doesn't this proof need one more rather trivial case? I believe this is only valid for M
It’s basically how the set is defined; by definition of m = n, the set is the empty set
@@drpeyam I thought about it again and there is technically enough math to extend it to M=N but there wasn't an explicit statement. Your inductive proof was valid from M€[0,N-1] however because of that, M+1 or M=N is also valid
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Hi Dr Peyam, i love your vids, greetings from Spain
Could you please talk indeep about dirichlet series?
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Very subtle, but great explanation. Thank you
Thank you!!!
First!