For the proof of spec(A*) we can first show that for some matrix M det(M*)=det(M)*. Please note * means conjugate of. This follows from Leibnitz formula and properties of conjugation. Using this fact we can show det(A*-sI)=det((A-s*I)*)=det(A-s*I)*=(s*-lambda1)*•••(s*-lambdan)*=(s-lambda1*)•••(s-lambdan*). So eigenvalues s=lambda*.
The best playlist so far for linear algebra.
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For the proof of spec(A*) we can first show that for some matrix M det(M*)=det(M)*. Please note * means conjugate of. This follows from Leibnitz formula and properties of conjugation. Using this fact we can show det(A*-sI)=det((A-s*I)*)=det(A-s*I)*=(s*-lambda1)*•••(s*-lambdan)*=(s-lambda1*)•••(s-lambdan*). So eigenvalues s=lambda*.
When will we reach tensors...
Tensors are higher dimensional matrices , right ?
@@eliasindbad8651 Yeah, kind of.
@@artophile7777 I hope I'll learn them soon
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thank you
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F1! F1! F1! It's gonna be so much fún!
Yes!
@@brightsideofmaths Machst du wirklich irgendwann mal Videos zu field with one element?! :D Das wäre der Wahnsinn!
If some people are interested.
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