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 Feb 8 asked If $T$ is an orthogonally diagonalizable linear operator in an inner product space, show that $T^*$ is also orthogonally diagonalizable. Feb 6 asked Let $\{e_1,\ldots,e_n\}$ be an arbitrary basis in a finite dimensional inner product space. Prove $\exists \{f_1,\ldots,f_n\}: (e_i,f_j)=\delta_{ij}$ Feb 4 asked What general mobius transformation maps $|z-1|=1$ to itself and $|z+1|=1$ to $|w-3|=3$. Feb 2 asked If $f$ is analytic in $D$ and $|f(z)| 1 \mid X_0 = X_1 = 0)$. Dec 13 asked Suppose $X_t$ is a brownian motion with $X_0 \sim u_0$. What is the probability density of $X_t$? (heat equation) Dec 10 asked Suppose $dX_t = a(X_t) dt + b(X_t) dW_t$ and $Y_s=X_t$ where $s=t^2$. What SDE does $Y_s$ satisfy in the weak sense? Dec 5 asked Is the determinant of $A$ is equal to the product of its eigenvalues for vector spaces over any field? Nov 22 asked What is the conditional distribution of $X_3$ where $dX_t = adt + dW_t$? Nov 20 asked How to solve the following PDE for A and B? Nov 19 asked Show $f_t- a x f_x + \frac{1}{2} b \sigma^2 f_{xx}=0$ has solutions of the form $f(x,t) = C(t) e^{-D(t)x^2}$ Nov 14 asked Find the limiting joint distribution of $X_n$ and $X_{n-1}$ as $n \to \infty$