Spectral theorem etc.

Dear Professor Kim,

I have looked at your course summary and I cannot find anything about the Spectral Theorem. The proof of this theorem was not covered in class, and in the online notes it only says “See the article ‘The Spectral Theorem’ on the course webpage”. I have however seen that a question on this proof in 2006 paper, so I was wondering if we need still need to know this proof? Also, do we need to know the extra material on the course webpage such as the supplementary notes and articles?

Best regards,

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Reply:

The course summary definitely mentions the spectral theorem: On the list at the end, it is theorem 5.5.159, whose proof, as you point out, is in the supplementary notes. I hope the summary and the course blog is making the relative importance of different portions clear enough. Essentially all the supplementary material should be useful.
But perhaps most relevant are:

– A practical summary of the course

-The spectral theorem

-Remark on quadratic forms

-The first two pages of `Supplementary note on self-adjoint maps’

and the various example sheets on Jordan canonical forms.

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