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Aug
11
comment Area between the curve and x-axis
Hi stuart, I see you have already asked a few questions, most of which have received good answers. If you're satisfied with an answer, you can not only upvote it, but also accept it by using the little check mark right below the up- and downvote arrows. This lets whoever answered your question know that you are indeed satisfied with the answer, and it helps people spot questions which still need more attention. :)
Aug
11
comment Differential geometry: $|\alpha(t)|=c\ne 0 \iff \langle \alpha(t),\alpha'(t)\rangle = 0,\forall t\in I$
Yes, both summands on the LHS of your equation are equal because of symmetry of the inner product, so they must both be zero. You can basically go along the exact same chain of thought - but backwards - to get the other direction of the statement you want to prove.
Aug
11
comment Linear map with polynomials - Find a matrix
That's correct. And what does a linear combination of the elements of the set $\{1,x,x^2,x^3\}$ look like?
Aug
11
comment Linear map with polynomials - Find a matrix
Do you see that $P_3$ is a vector space? Do you know what the definition of a basis of a vector space is? Can you write a general expression that every element in $P_3$ looks like?
Aug
10
comment Linear map with polynomials - Find a matrix
Do you know why $\{1,x,x^2,x^3\}$ is a basis of $P_3$? The strategy you use to find $A$ is usually the same: You apply $F$ on your basis and then see which matrix $A$ satisfies $A \cdot v = F(v)$ for all $v$ in your vector space. The matrix corresponding to a linear map depends on a basis - thus if you take a different basis in ii), you will have a different matrix $A'$. My answer here might be helpful: math.stackexchange.com/a/1087851/3787
Aug
7
comment English translation of von Neumann's “Zur Theorie der Gesellschaftsspiele”, 1928
I'm afraid I can't since I haven't read it myself. My game theory course was in German, so we used German books/articles. Are you just interested in learning some basic game theory in general or do you absolutely want to read about it from Von Neumann?
Aug
7
comment Multiplications in determinant of an $n \times n$ matrix?
If you don't know what the notation $\mathcal{O}(N^3)$ means, check out this: en.wikipedia.org/wiki/Big_O_notation
Aug
7
comment Example of a nowhere dense subset of a metric space.
What's the closure of $\mathbb{Z}$? What's its interior?
Aug
7
comment How did Euler give a sum to the divergent series $…x^{-3}+x^{-2}+x^{-1}+1+x^1+x^2+x^3.. = 0$?
How is this supposed to hold for any $x > 0$? All summands are strictly positive, so their sum surely can't be $0$?
Aug
5
comment Jänich linear algebra, Question 2.3 solution clarification
Take $U_1 = U_2 = \{0\}$. Is $(U_1 \cup U_2) \setminus U_2 = U_1$?
Aug
3
comment What is the difference between the following $2$ sets?
What is the difference between $[1+\delta, \infty)$ and $(1,\infty)$? Does one of them contain the other?
Jan
9
comment How to say if Eigenvectors of A are orthogonal or not? without computing eigenvectors
@Andy: en.wikipedia.org/wiki/Symmetric_matrix#Real_symmetric_matrices
Jan
9
comment How to say if Eigenvectors of A are orthogonal or not? without computing eigenvectors
Do you know the Spectral theorem?
Jan
7
comment Predicates and Quantifiers in discrete math
What have you tried so far?
Jan
5
comment Generic method to find a matrix whose null space is given
@Dor: I'm not sure I understand your question. We know we can write $A$ in such a form (with only non-zero elements in one row). By multiplying $A$ with the two vectors $v_1, v_2$ and setting it equal to zero I constrain $A$ such that $\ker(A) = \operatorname{span}(v_1,v_2)$. Does that answer your question? If not, could you try to rephrase it?
Jan
4
comment Eigenvalue of the substraction of 2 matrices
If you have to prove or disprove the statement "If $A$ and $B$ have the same eigenvalues, then $A-B$ has eigenvalue $0$", then one counterexample is sufficient to disprove the statement. If you want to prove that the statement is true, you'll need to show it for general matrices $A$ and $B$ and not just using one example.
Jan
3
comment $0$ and $p^n \mathbb{Z}_p$ are the only ideals of $\mathbb{Z}_p$
@fretty: $n$ can be $0$.
Jan
3
comment Diagonalization versus s.d. product for non-commuting Hermitian matrices
@nomadreid: Yes, they are equivalent, which is what I have shown in my post. First, I have shown that $[A, B] \neq 0$ is equivalent to (1) and then, I have given you the theorem that it is also equivalent to (2). Because equivalence of statements is an equivalence relation, (1) and (2) are equivalent to each other. This also applies to your third point: The point of my post was to show that (1) and (2) are not just consequences of $A$ and $B$ being non-commutative, but all three statements are equivalent!
Jan
2
comment Diagonalization versus s.d. product for non-commuting Hermitian matrices
@nomadreid: Which bases do you mean? My point was that both statement (1) and (2) are equivalent to $[A,B] \neq 0$, in case it wasn't clear. I thought you were trying to understand how one comes up with these two results.
Jan
2
comment If A is an open set does A the complement of A have to be closed? I know the opossite is true by definition, is this?
A set is closed if its complement is open.