Functional Analysis 28 | Spectrum of Bounded Operators

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This is my video series about Functional Analysis where we start with metric spaces, talk about operators and spectral theory, and end with the famous Spectral Theorem. I hope that it will help everyone who wants to learn about it.

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#FunctionalAnalysis
#VectorSpaces
#Mathematics
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I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[deph__]

So glad that you're making a serie about Spectral Theory, I'm not quite there yet in my studies but I was always fascinated by the topic. Your videos really inspire me to study math even more.

[ottoomen]

This is an excellent introduction. The video is a moderately advanced introduction, although spectral theory is an advanced topic. Excellent work.

[வெற்றி-னள]

I am electrical engineer. Took course in spectral analysis. What you taught is similar to the basics of our course. The beauty is the concepts you taught can be used to compute pseudoinverse for non square matrices. This has applicatioms in detection amd estimatiom

[tungvuthanh]

Thank you for the lecture I have been struggle with the math behind Quantum Mechanics for a long time. The topics is very well explained

[princesaha]

Great man, keep going please complete the spectral and other important theorems fast, also your search result is almost top in India so don't worry you will get lots of views once syllebus is completed, I did not much of measure they your lectures were blessing 😊😊

[rrrrupan]

Please continue your teaching towards Pure 🎉❤

[dieterziehe]

I have to say the same as Dywww. Thanks for your presentation. Where did you do your presentation normally (on which University)? Best regards. Dieter

[댕댕이-ci]

I look forward to seeing next lecture!!

[_Cristina]

I really wanted to watch your videos, but your channel doesn't have subtitles turned on to allow the inclusion of more people ):
I hope you read this and that when I come back I can be part of your subscribers.

[ketansutar]

Thank you sir..
Waiting for the next video with some fascinating examples and your always inspiring explanation...😇😇😇

[weirdo-jwkc]

Excellent. But I have a question. If the spectrum consists of both countable and Continuum eigenvalues then what is the dimension of the Banach space is it countable or uncountable? Actually I'm from physics background and we use position and momentum basis where the spectrum is Continuum. But there are other operators (self adjoint) for the same system whose spectrum is countable and their eigenvalues forms a complete set. So what is the dimension of the space?. Also I have another request can you do separate video on topological vector spaces. The book I'm reading starts with it but I don't see using that later in the book. So can you explain how topological vector space plays a role in functional analysis? Thank you.

[eliasmai]

Can you also do some lecture videos on topological vector spaces within functional analysis please. :)

[ValorantClipsAllDay]

Came expecting the spectrum operator from valorant… stayed for an educational video