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 Aug 11 answered Area under a curve subintervals 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 answered Differential geometry: $|\alpha(t)|=c\ne 0 \iff \langle \alpha(t),\alpha'(t)\rangle = 0,\forall t\in I$ 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 10 awarded Civic Duty 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 answered English translation of von Neumann's “Zur Theorie der Gesellschaftsspiele”, 1928 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 5 answered Explanation of this integral's solution Aug 3 accepted Proving that the coordinate basis is a basis of a tangent space 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? Aug 3 reviewed Edit $A$ is a $n \times n$ matrix over $\mathbb{R}$ such that $A^2+A+5I=0$. Find the characteristic polynomial of the matrix $A$. Aug 3 revised $A$ is a $n \times n$ matrix over $\mathbb{R}$ such that $A^2+A+5I=0$. Find the characteristic polynomial of the matrix $A$. added 7 characters in body; edited title Aug 3 revised Proving that the coordinate basis is a basis of a tangent space deleted 10 characters in body Aug 3 asked Proving that the coordinate basis is a basis of a tangent space