Abstract Linear Algebra 48 | Proof of Spectral Theorem [dark version]

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🌙 There is also a dark mode version of this video:    • Abstract Linear Algebra 48 | Proof of Spec...  
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This is my video series about Abstract Linear Algebra. It extends the Linear Algebra series by considering more general vector spaces. We will discuss abstract vector spaces, abstract inner products, the change-of-basis matrix,different bases, polynomial spaces, and so on. I hope that it will help everyone who wants to learn about it.
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00:00 Introduction
00:40 Statement: Spectral Theorem for Normal Matrices
01:37 Proof of first implication
04:15 Proof of second implication
06:15 How do normal triangular matrices look like?
08:31 Induction proof that normal triangular matrices are diagonal
12:06 Correction: here we already use w = 0 for the matrix product of R*R!
12:27 Using the induction hypothesis
13:45 Outro and credits

#LinearAlgebra
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#calculus
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