Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Vector]

.

[ZetaX]

You could use any algorithm that works for reals as long as that algorithm didn't somewhere use that 2 \neq 0 or that you have a notion of being positive, with the added bonus that you won't encounter numerics. Especially, I don't see why LUP should not work. You should be able to solve your equation in O(n^2.376), n the dimension, or whatever better algorithm is already known.

[i2amroy]

Can someone tell me, conceptually what eigenvalues and eigenvectors are? I can work the math and find them, but it's difficult to see how to use them, remember the formulas if I'm not sure what they are supposed to represent.

[MagmaMcFry]

Can someone tell me, conceptually what eigenvalues and eigenvectors are? I can work the math and find them, but it's difficult to see how to use them, remember the formulas if I'm not sure what they are supposed to represent.

Okay, so you have a linear function that maps things onto the same kind of things. Then an eigenthing is a thing that gets mapped onto a multiple of itself. And the eigenvalue is how multiple it gets made. So if you have a square matrix that maps vectors onto vectors by left-multiplication, then the eigenthings are called eigenvectors.

[i2amroy]

Ok, that makes much more sense now. Thanks.

[Vector]

.

[Helgoland]

Does anyone have pointers to a good introduction to homology? My prof went through the technical details at a rapid pace, and I failed to keep up - and now I'm lost. Badly.

[ZetaX]

Does anyone have pointers to a good introduction to homology? My prof went through the technical details at a rapid pace, and I failed to keep up - and now I'm lost. Badly.

What kind¿

[Helgoland]

What kind of homology? Singular, I guess. But knowing about the others wouldn't hurt either.

[ZetaX]

So of topological spaces (there are others, e.g. of chain complexes, giving rise to what is called homological algebra). Then I would recommend Hatcher's Algebraic Topology (should be chapter 2). It has lots of exercises and is one of the more elaborate books I am aware of.
In case you want to look at chain complexes and such (the methods are over all of mathematics, especially algebraic topology and geometry), I know that Weibel's Introduction to Homological Algebra is fine, but be warned that this subject, while not difficult, can get quite lengthy. Due to its nature, reading lots of homological algebra at once may be a bit dull, a lot of people learn it simply "along the way". I don't have the book at hand to point out the most relevant chapters, but everything about homology of complexes is relevant, and taking a look at the chapter concerned with simplicial methods might be a good idea after having seen simplicial homology in topology.

As mentioned there are others, e.g. group (co)homology or étale cohomology, but I would advise understanding one of the more basic ones above first.

[Helgoland]

Thanks! I actually have chapter two of Hatcher's Algebraic Topology open in another tab

[Descan]

Can someone tell me how the integral of r^(4/7) (or fourth-root of r^7) is

(4/11)* r^(11/4) + C

Both my book and Wolfram Alpha tell me that it's something like that, while basic sense and another calculator tell me it's

(7/11) * r^(11/7) + C

[MagmaMcFry]

Can someone tell me how the integral of r^(4/7) (or fourth-root of r^7) is

(4/11)* r^(11/4) + C

Both my book and Wolfram Alpha tell me that it's something like that, while basic sense and another calculator tell me it's

(7/11) * r^(11/7) + C

What are you putting into WA? Because my WA query gave me the bottom expression like it should.

[Descan]

Okay, now WA is giving me the proper one, but the book is still wrong and I don't know if it's just a mis-print or if I'm missing something sneaky. :V

[frostshotgg]

Can someone tell me how the integral of r^(4/7) (or fourth-root of r^7) is

(4/11)* r^(11/4) + C

Both my book and Wolfram Alpha tell me that it's something like that, while basic sense and another calculator tell me it's

(7/11) * r^(11/7) + C

7/11 * r^(11/7) + C should be correct. Derivative is 11/7 * 7/11 * r^(4/7) dr.