Eigen Values and Eigen Vectors: Visually Explained!

dexterdev (62) in steemstem • 7 years ago (edited)

View this post on Hive: Eigen Values and Eigen Vectors: Visually Explained!

7 years ago by dexterdev (62)

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mathowl (64) · 7 years ago

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.

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1 vote

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dexterdev (62) · 7 years ago

I should look into fibonacci map. It seems interesting. :)

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gentleshaid (70) · 7 years ago

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

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dexterdev (62) · 7 years ago

@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.

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gentleshaid (70) · 7 years ago

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.

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dexterdev (62) · 7 years ago

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

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gentleshaid (70) · 7 years ago

Thanks a bunch for this. I hope professors in my school will imbibe this idea

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dexterdev (62) · 7 years ago

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

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gentleshaid (70) · 7 years ago

Yea... One of the college's isn't far from my base.

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physics.benjamin (54) · 7 years ago

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!

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dexterdev (62) · 7 years ago

Thank you for reading. I am happy if this helped. :)

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anevolvedmonkey (53) · 7 years ago (edited)

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.

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dexterdev (62) · 7 years ago

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.

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midfrost (33) · 7 years ago

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?

🙏

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dexterdev (62) · 7 years ago (edited)

superdeterminism? Can you elaborate? Yeah at times I used to fancy that pilot wave theory becomes successful.

so if I understand it correctly, each dimension is essentially an "eigen vector", no?

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.

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tibra (58) · 7 years ago

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.

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midfrost (33) · 7 years ago

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."

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dexterdev (62) · 7 years ago

How you know I like this idea?

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midfrost (33) · 7 years ago

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. 🙏

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dexterdev (62) · 6 years ago

so if I understand it correctly, each dimension is essentially an "eigen vector", no?

I think you can so too!

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sathyasankar (63) · 7 years ago

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.

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dexterdev (62) · 7 years ago

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.

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vinamra (54) · 7 years ago

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.

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dexterdev (62) · 7 years ago

This article is self-contained. You can have a visual glimpse of eigen stuff from here. This is not a rigorous article though. :)

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dexterdev (62) · 7 years ago

@mathowl

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mathowl (64) · 7 years ago

I guess I need to make an educational owl first :P

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