Oliver Jones
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 Feb 14 comment Problem 10 chapter 9 from PMA Rudin You need $g$ to be differentiable on your interval $(b_1, a_1)$ but this assured by the existence of $D_1f$ on $E$. You don't need $(D_1f)(u,a_2,\cdots ,a_n)=0$. Feb 12 comment Problem 10 chapter 9 from PMA Rudin This proof looks fine. You should probably mention why $g(t)$ satisfies the conditions of the Mean value theorem. Feb 10 revised Conjugating rotation by another rotation deleted 715 characters in body Feb 10 revised Conjugating rotation by another rotation added 606 characters in body Feb 10 revised Conjugating rotation by another rotation added 606 characters in body Feb 9 comment Common Intersection Point of ellipsoids @fuzzyrock1 I know what you mean but you must describe the condition mathematically. Feb 8 comment Existence of a block upper triangular form matrix representation for a linear operator Think about what $[T]_{\cal B}$ means. Feb 8 comment Existence of a block upper triangular form matrix representation for a linear operator You're right; $T$ would need to be normal. But orthogonality isn't needed to prove the result. Feb 8 comment Existence of a block upper triangular form matrix representation for a linear operator Because of orthogonality. Feb 8 comment Existence of a block upper triangular form matrix representation for a linear operator Won't $B_2$ be $T$-invariant? Feb 8 comment Area inside polar curve There are two solutions. Feb 8 comment Area inside polar curve You need to solve $7\sin \theta =1$. However, these will not be nice angles and so you have to express them in terms of $\sin ^{-1}$. Feb 8 comment Existence of a block upper triangular form matrix representation for a linear operator If you extend to an orthonormal basis for $V$ then you get block diagonal form, not block upper triangular form Feb 8 comment Existence of a block upper triangular form matrix representation for a linear operator Start with a basis for $W$ and extend it to a basis for $V$. Then use the fact that $W$ is $T$-invariant. Feb 8 comment Area inside polar curve Arc length has nothing to do with area. Start by finding the intersection points of both curves. Feb 8 comment Definition of Inverse in Linear and Abstract Algebra For the second problem concerning the homomorphism, you already know that the inverse exits because you are in a group. Proving $\phi (a^{-1})=[\phi(a)]^{-1}$ is not equivalent to proving an inverse exists. Feb 8 comment Spectral norm of lower triangular perturbation You have that $L=A-I$ and so $\lVert L \rVert \le \lVert A \rVert +1< 2+\epsilon$. Feb 8 comment Common Intersection Point of ellipsoids @fuzzyrock1 You need to define the condition "unless one is contained in the other". Feb 8 comment Common Intersection Point of ellipsoids You need to formulate your condition in terms of major and minor axes. Feb 8 comment Polar Equations (Complex) If it's correct, you will need to use a calculator.