Eigen Values and Eigen Vectors: Visually Explained!
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6 years ago in #steemstem by dexterdev (62)
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Content type: long, educational
Awarded 3.5 out of 6 owls:
Details: The spelling and grammar was not awarded since the post contained quite a few mistakes related to particles and articles (one in which obeys-> one which obeys, That is you divide by the magnitude of the vector -> That is when you divide by the magnitude of the vector then.. etc.) The originality owl was not awarded since it requires content to be explained in a novel way. Only have half an education sensation owl was awarded since there are more engaging ways to explain this. For example, you can define the fibonacci map as a matrix. You then find that one of the eigenvalues is equal to the golden ratio.
I should look into fibonacci map. It seems interesting. :)
Mathematics is quite an interesting subject especially, it's applications. I'm a biologist anyway, unless we are talking about statistics and modelling, I might have nothing to do with maths
@gentleshaid : In computatyional biology, mathematical biology, systems biology and biophysics etc the concept of eigen values and vectors pops up multiple times. A lot of mathematical applications are possible. If we are able to make sense out of applying math in biology, that is a great thing. For example the field I am working in is called Molecular dynamics, where I try simulating proteins, which is only possible because we are applying physics which in turn uses concepts from mathematics (applied math) too. Recently we are seeing a trend in most biology labs. Biology is getting more quantitative in nature, which is a great sign.
That's an aspect I would like to explore but I'm afraid of where to start from really. I've not done much mathematics, just a little statistics. I deal mostly with ecological aspect of the environment especially as it relates to plant. In the process of getting PhD in it actually. I have a long way to come from in mathematical biology.
I understand you. The best thing which people do these days is bringing up an interdisciplinary group. Like a biology professor will have a student trained in electronics or physics who are interested in biology and a post-doc who was a string theorist in past. I am not naming people here. This is very common these days. Even In India! And there are multiple workshops which enable people from multiple backgrounds to enable them to talk to each other. This is such a workshop : https://www.icts.res.in/program/qsb2017
Thanks a bunch for this. I hope professors in my school will imbibe this idea
If you see the participants, you can see Nigerian students in this link. Do you know these colleges? https://www.icts.res.in/event/page/12388
Yea... One of the college's isn't far from my base.
Yes Dexterdev, this actually helped to visualize this in my minds eye. I approach physics on trying to understand it in my "minds eye" first and this is cool man. Good job! Thanks a lot!
Thank you for reading. I am happy if this helped. :)
Ah, linear algebra, the subject which most people don't understand but can solve the problems easily.
Nicely done! and I am so happy to see Gilbert Strang on the reference list. The MIT courseware on linear algebra by this guy is pure gold! I mean I want to unlearn linear algebra and watch those lectures again.
Cool. Math was really taught very badly when I was young. And I am happy that people have more resources now to get quality study materials.
I know you wrote physics as well as applied mathemathics, so perhaps you'd be rather unwilling to share with me your thoughts on the subject "Superdeterminism"?
Thank you for this very informative post though, so if I understand it correctly, each dimension is essentially an "eigen vector", no?
🙏
superdeterminism? Can you elaborate? Yeah at times I used to fancy that pilot wave theory becomes successful.
No. If you are working in a 2D space, there will be 2 eigen vectors corresponding to any operation A you do on a vector X. That means the number of eigen vectors you can obtain in a N-D space in N. (N is the dimension). That doesn't mean each dimension is one eigen vector.
You should check out Basil Hiley's papers on quantum blobs, if you're interested in deterministic theories. He and Bohm and Penrose had a group when they were at the same institution.
Superdeterminism (wikipedia link).
But to simplify the concept with the words of the late Mr. Einstein,"I do not believe God played dice with the Universe."
How you know I like this idea?
I didn't, until just now, but I like it myself, and therefore did I want to hear your thoughts on it... to gain perspective. 😊🌠
In my way of reasoning, it was not my doing in the first place, whom- or whatever decided to raise the subject.
Eye do not consider myself an agent of volition. 🙏
I think you can so too!
So, for eigen vectors to come into play the lines must be linearly independent of each other, especially orthonormal..Isn't it?
The fault of our education system lies in its reluctance to reveal the applicability of any theory..I haven't known that Eigen values & Vectors have the pragmatic operations even in Google! Interesting.
The eigenvector pair in 2d will be orthogonal. If it is N dim then those N vectors would be orthogonal. Yeah they have lot of applications.
Well dev....no comments!
It's way beyond me.. :)
I only have a glimpse of the eigenvalue, when it came as a short course in my masters and that time also I didn't learn it properly.
This article is self-contained. You can have a visual glimpse of eigen stuff from here. This is not a rigorous article though. :)
@mathowl
I guess I need to make an educational owl first :P