Actually, this is more of a general question relating to a homework problem I already did. I was given the initial wavefunction of a particle in an infinite square well:
\Psi(x,0) = Ax if (0 \leq x \leq \frac{a}{2}), and =A(a-x) if (\frac{a}{2} \leq x \leq a)
And of course \Psi(0,0) =...
My textbook states that for operators on complex vector spaces with dimension greater than one, and real vector spaces with dimension greater than two, that there will be invariant subspaces other than {0} and V.
Maybe the book means for a particular operator?
Homework Statement
Prove or give a counterexample: If U is a subspace of V that is invariant under every operator on V, then U = {0} or U = V. Assume that V is finite dimensional.
The attempt at a solution
I really think that I should be able to produce a counterexample, however...
Homework Statement
Give a specific example of an operator T on R^4 such that,
1. dim(nullT) = dim(rangeT) and
2. dim(the intersection of nullT and rangeT) = 1
The attempt at a solution
I know that dim(R^4) = dim(nullT) + dim(rangeT) = 4, so dim(nullT) = dim(rangeT) = 2.
I also...
ok, but can I at least write a basis for null(T) and range(T)? I can't see how to prove this without defining something, because I know I can't prove this by only referring to the finite dimensions of null and range.
Homework Statement
Prove that if there exists a linear map on V whose null space and range are both finite dimensional, then V is finite dimensional.
The attempt at a solution
I *think* the following is true: For all v in V, T(v) is in range(T), otherwise T(v) = 0 which implies v is in...
Gosh, I must be getting sleepy to overlook the importance of n being unique.
So, I can show that each element of V can be written uniquely as a sum of u + n.
Should I also prove U = {au : a is in F} is a subspace of V
n and n' could definitely be different, but I don't think it matters much since they both get mapped to zero.
Is the result of a = a' is enough to prove uniqueness for a direct sum?
if V were finite dimensional then I could say, dim{null(T)} = dim(V) - dim{range(T)}.
But nothing given in the problem statement will let me assume V is finite.
Homework Statement
Suppose that T is a linear map from V to F, where F is either R or C. Prove that if u is an element of V and u is not an element of null(T), then
V = null(T) (direct sum) {au : a is in F}.
2. Relevant information
null(T) is a subspace of V
For all u in V, u is not...
I was wondering if anyone knew anything about epidemic models which take into account the ability of a disease to mutate. Basically I’m curious if there are any existing models which could predict how a rapidly changing disease might affect the progression of an epidemic, or how slower...
Ok, I went into my maple worksheet and chose to export my graph as an .eps, but the file says that it is postscript. I'm also very confused by some of the instructions on the links. For example at
http://amath.colorado.edu/documentation/LaTeX/reference/figures.html
In the 'Only...
I included all those commands, but I still got the same warning and error.
What's the difference between .ps and .eps and why would latex require me to use .eps?
Latex gave me one warning and one error.
Latex warning: file 'myfile.ps' not found on line41
! Latex error: unknown graphics extention: .ps
I did use \usepackage{graphicx} in my document, I just typed it wrong in this thread.
And as far as having a graphics package instaled, I'm...
hi,
I'm trying to put a graph generated in maple into a latex document, but I have no experience using either program. So far I've been able to save my maple plot in postscript format, and based on various online tutorials I've included the \usepackage{graphics} comand after...
Since u and v are elements of the intersection, u and v will also be elements of any subspace W that is in the intersection. And since u and v are in W and W is a subspace, this guarantees that u+v will also be in W. This same argument would apply to scalar multiplication.
Is that the...
Prove that the intersection of any collection of subspaces of V is a subspace of V.
Ok, I know I need to show that:
1. For all u and v in the intersection, it must imply that u+v is in the intersection, and
2. For all u in the intersection and c in some field, cu must be in the...
Homework Statement
Prove: If a, b are nonzero elements in a PID, then there are elements s, t in the domain such that sa + tb = g.c.d.(a,b).
Homework Equations
g.c.d.(a,b) = sa + tb if sa + tb is an element of the domain such that,
(i) (sa + tb)|a and (sa + tb)|b and
(ii) If f|a and...
Homework Statement
Let G_1 and G_2 be groups with normal subgroups H_1 and H_2, respectively. Further, we let \iota_1 : H_1 \rightarrow G_1 and \iota_2 : H_2 \rightarrow G_2 be the injection homomorphisms, and \nu_1 : G_1 \rightarrow G_1/H_1 and \nu_2 : G_2/H_2 be the quotient epimorphisms...
What are you trying to solve? You could substitute numbers for the x's and compute the value.
I don't believe there's a nifty identity for (sin(3x))^2 + (cos(3x))^2 even though it does look somewhat similar to (sin(x))^2 + (cos(x))^2.
Ironically, the book is called 'Linear Algebra Done Right' 2nd ed. by Sheldon Axler. I don't exactly love it, but it is what I'll be using this fall so I better get used to it. :rolleyes:
Thanks for all the help!
The book I'm working from does not discuss infinite dimensional vector spaces. It only gives a brief description of $\mathbf{F}$^{\infty} and P(F), the set of all polynomials with coefficents in $\mathbf{F}$.
In particular it says, "because no list spans P(F)...
Prove that $\mathbf{F}$^{\infty} is infinite dimensional.
$\mathbf{F}$^{\infty} is the vector space consisting of all sequences of elements of $\mathbf{F}$, and $\mathbf{F}$ denotes the real or complex numbers.
I was thinking of showing that no list spans $\mathbf{F}$^{\infty}, which would...
Well, in question B. they ask for the spring force which is in units of Newtons.
The units in your answer are in joules, but you need them to be in Newtons in order for the answer to make sense.
We don't do that here.
However, if you show the work you've already done on this problem, people will point out your mistakes and help you solve your own problem.
First ask yourself why you believe this would actually happen.
Why would the teen time be less than the adult time?
The answer to this question should also give you some ideas for a keyword search.
HA! His fabulous cooking is no match for me! I just act like I have no will of my own.
Reverse psychology: He thinks he has superpowers, I get fed, and it insures more fabulous meals in the future! :wink:
Shhh... don't tell Tom, he might stop cooking for me.
Well, when a girl scientist and a boy scientist like each other a lot, they try to impress one another with their intelectual prowess.
If their witty banter goes well they exchange tokens of their mutual affection (such as a calculator or a Schaum's outline).
If they stay together long...
You just had to drag me into this :grumpy: didn't you. I'm going to stuff you into a cannon and find out how far you fly!
"Oh, wait, MIH, once you get him in your sights, if he's cute, don't shoot! "
He won't be so cute after I launch him across the Hudson river :devil:
Look in the section of the book which is associated with that homework set.
'Usually' the information you need is contained in the chapter preceding the question.
What topics are you currently learning from your textbook?
Don’t be afraid to post something; people on this forum are here to help, not judge. Besides, that’s the beauty if the internet… It’s anonymous. :biggrin:
"but i didnt make a separate thread abouut it coz moderators wouldn't like it"
There would be no point in starting another thread on the same topic.
"i have focused my paper on technical and logical aspects of it"
I didn't catch this the first time through. It sounds like you're well...
How is it that you have written 7 pages when you do not yet have a thesis statement, a basic outline of what sub-topics you want to discuss,
or any idea as to how you want to structure your discussion? :confused:
There is nothing that tells us 'things must obey these descriptions' absolutely every single time. This is the big difference between science and other explanations (ie religion) for the state of the world around us. Scientific theories must be falsifiable. When we observe something which...
hi,
I'm doing some of the same stuff in my analysis class, and in my class notes the teacher wrote that sin(x) = O(x), not x^2.
Going back to the definitions of 'little o' and 'big O' might help.
f = O(g) means that the ratio of f/g is bounded by some constant, where f = o(g) means...
Evil trees? o:)
Actually, I'm curious. What is your definition of evil?
I don't think I could really comment on the 'cause of all evil' without knowing your definition of evil itself.
You could try the math and science tutorial section, or the links here at PF. I don't know if there would be any audio tutorials.
You might want to check out your community or university library. Also, try asking local bookstores if they carry such products.
The first physics course I ever took used the 'pre-edition' of Knight's book. The text was free but it was AWFUL!
The next semester I was required to buy the 1st ed. of the Knight book. The stupid thing was still chock full of typos and unclear language.
And worse than typos; in the...
hi,
In the course of doing my quantum homework I ran into a bit of a snag.
In one of my calculations I need to replace the sum from n = 1 to infinity of 1/n^2 (for odd n only) with its number value.
My book instructs me to get the information from a table and actualy gives the value (for...
Try drawing two pictures; the first showing the initial conditions, and the second showing the final conditions when you've caught the bus.
Once you've drawn the pictures, make sure you listed all your knowns.
List your kinematics formulas so you can see what you have to work with...