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1. I Interpreting The Definition of Tensors

I apologize for my ignorance , but I'm not sure what you mean by copies of a vector space? So taking the inertia tensor as an example: $$\mathbf{\widetilde{I}} = \int dm \left[ <r|r> \mathbf{1} - |r><r| \right]$$ How does the idea of it being a linear combination of outer products of...
2. I Interpreting The Definition of Tensors

But one needs to understand the mathematical operations being performed to be able to understand how said mathematical entity remains unchanged through a sequence of operations. Yes, I'm fully aware, the magnitude/direction of a vector under these types of linear transformation doesn't change...
3. I Interpreting The Definition of Tensors

Hello, I've just been slightly unsure of something and would like to get secondary confirmation as I've just begun a book on tensor analysis. I would also preface this by saying my linear algebra is somewhat rusty. Suppose you have the inertia tensor in some unprimed coordinate system such that...

Also Pi day.
5. A quick question regarding undergraduate research

Not at all! Your comment was certainly helpful in it's own way. Thank you very much !
6. A quick question regarding undergraduate research

Thanks! This was incredibly helpful. I do think that it probably can double as an AFM as from what I've heard it's a high-grade STM. The deed is done, fingers crossed.
7. A quick question regarding undergraduate research

Hi there, so my friend and I recently asked our professor to allow us to do research with her, whatever that entails. She requested that we submit a CV and a short e-mail to her. This is my first time doing this sort of thing so I'm completely clueless in regards to what a professor might find...
8. What's the most impressive/useful/interesting invention? (that hasn't been invented yet)

Given the axiom of heat death or some other form of an equally destructive event, everything is a matter of longevity. I don't quite understand what you're trying to say . How is it a non-starter? All you have to do is cure aging and most fatal diseases. Unless you're an indestructible...
9. What's the most impressive/useful/interesting invention? (that hasn't been invented yet)

He said immortality not invincibility. There is a distinction to be made here. Immortality is the ability to live eternally given the chance, but if I stab you to death you will die. Invincibility on the other hand is a little similar what you're describing, indestructiblity. If you hit a...
10. I Which tank fills first

Tank F. Edited: missed a tiny detail.
11. I Free pdf for PDE on AMS Open Math Notes

Thanks! What I needed exactly when I needed it!
12. I When is a Constant a Solution to a Differential Equation

I'm self-taught on this topic, so take what I say with a grain of salt. But here's what I was referring to: https://en.wikipedia.org/wiki/Singular_solution "Therefore, when one is solving a differential equation and using division one must check what happens if the term is equal to zero, and...
13. I When is a Constant a Solution to a Differential Equation

I misunderstood your question, my apologies.
14. I When is a Constant a Solution to a Differential Equation

When you solved the differential equation you had to divide both sides by x, since x ≠ 0, x=0 will be omitted from your general solution by default. Remember to write your restrictions, because it's impossible to get singular solutions by varying the parameters of your general solution as far...
15. Non-Science Podcasts

Not quite sure what you mean by extensionists, Perhaps you should elucidate? Do you mean that they unnecessarily try to spawn content from oblivion to tack on a few minutes onto the episode?
16. Non-Science Podcasts

Totally agree, he's very good at asking challenging questions and genuinely puts effort into probing the subject at hand with the interviewee. A very intellectually stimulating podcast to say the least.
17. Non-Science Podcasts

•HI (Hello Internet) •Cortex •Wakiping Up (Warning: somewhat political and science related ) •No Dumb Questions •Dan Carlin's Hardcore History These are currently my favorite non-science podcasts which I listen to on a regular basis. I'm on the opposite side of the fence as of now, I'm looking...