Abstract Linear Algebra 11 | Positive Definite Matrices [dark version]
ฝัง
- เผยแพร่เมื่อ 7 ก.ย. 2024
- Find more here: tbsom.de/s/ala
Support the channel on Steady: steadyhq.com/e...
Or via other methods: thebrightsideo...
Or support me via PayPal: paypal.me/brig...
Or via Ko-fi: ko-fi.com/theb...
Or via Patreon: / bsom
Or via TH-cam: / @brightsideofmaths
Watch the whole video series about Abstract Linear Algebra and download PDF versions and quizzes: tbsom.de/s/ala
There is also a dark mode version of this video: • Abstract Linear Algebr...
There is also a bright mode version of this video: • Abstract Linear Algebr...
To find the TH-cam-Playlist, click here for the bright version: • Abstract Linear Algebra
And click here for the dark version of the playlist: • Abstract Linear Algebr...
Thanks to all supporters! They are mentioned in the credits of the video :)
This is my video series about Abstract Linear Algebra. 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.
For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: tbsom.de/s/com...
#LinearAlgebra
#FunctionalAnalysis
#Mathematics
#LearnMath
#calculus
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)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here tbsom.de/s/start
![Abstract Linear Algebra 12 | Cauchy-Schwarz Inequality [dark version]](http://i.ytimg.com/vi/P55SZr83LVQ/mqdefault.jpg)
![Abstract Linear Algebra 12 | Cauchy-Schwarz Inequality [dark version]](/img/tr.png)
![ตีสิบเดย์ [FULL] | นางเอกหมอลำเงินล้าน "อุ๋งอิ๋ง เพชรบ้านแพง" & ไฮโซสาวสุดฮอต "ลิลลี่ เหงียน"](http://i.ytimg.com/vi/jPxQS_EgrJ4/mqdefault.jpg)
awesome im taking this class rn
Have fun! :)
Thank you very much for the interesting and knowledge-filled videos,
I have a question, please. Regarding positive operators, why must operator A be selfadjoint? Isn’t it enough for the inner product to just be positive?
Many thanks.
The selfadjointness guarantees that the inner product (in this form) is always a real number. Only for real numbers, the notion "positive" makes sense :)
thank you very much for this important remark, now I understand well. Indeed, French-speaking courses do not add the condition of self-adjoint to define a positive operator, so your definition, which I find coincides in all English-speaking works, is well justified by your explanation.
@@brightsideofmaths -- Very incidentally, standard English actually uses German-like "V2" syntax in cases like your last sentence.
That is, it puts a verb (well, a helper verb) in the second slot ("Linke Satzklammer"):
(Only for real numbers) (does) (the notion "positive" make sense.)
According to the Wikipedia article on "V2 word order", in cases of "negative or restrictive adverbial[s]", English maintains V2 as a vestige of its Germanic roots.
Other examples:
(At no point) (will) (he drink Schnapps.)
(No sooner ) (had) (she arrived) (than she started to make demands.)
I know grammar's off-topic, but I thought you might find this tidbit helpful or interesting, given your German fluency.
I find this really interesting. Which of the two versions of my sentence would you prefer? Does my sentence even sound wrong for native English speakers? I actually wrote your version first and corrected it because I thought it was my German brain making grammar mistakes.
Nice 👍
Thank you! Cheers!