# Recent content by *melinda*

1. ### Length of an infinite square well?

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) =...
2. ### Linear Algebra: Invariant Subspaces

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?
3. ### Linear Algebra: Invariant Subspaces

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...
4. ### Specific Linear Map Example

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...
5. ### More linear maps

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 refering to the finite dimensions of null and range.
6. ### More linear maps

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...
7. ### Linear Algebra, Linear Maps

:zzz: I should be able to stay awake long enough to write down my solution. Thanks for the help!
8. ### What's the integral of u''(x)/u'(x)?

you need to do u substitution
9. ### Linear Algebra, Linear Maps

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
10. ### Linear Algebra, Linear Maps

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?
11. ### Linear Algebra, Linear Maps

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.
12. ### Linear Algebra, Linear Maps

1. 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...
13. ### Epidemic models which incorporate disease evolution

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...
14. ### LaTeX Including graphics in LaTeX Help!

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...
15. ### LaTeX Including graphics in LaTeX Help!

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?