Beacon
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1 answers
5 votes
90 views
Ring theory: Prove if $g \in \mathcal{B}$, then $g=f_1 h_1+...+f_nh_n$ for some elements $h_1,...,h_n$ in $A$.
2 answers
4 votes
40 views
2 bookmarks
Invertible matrix($T:M_{2*2}(R) \rightarrow M_{2*2}(R)$ defined by T( $\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$
1 answers
3 votes
75 views
1 bookmarks
Parking function problem
1 answers
2 votes
100 views
Prove that $U(E_{\lambda})=E_{\lambda}$ and $U(K_{\lambda})=K_{\lambda}$.
1 answers
2 votes
75 views
1 bookmarks
Prove there exists an orthonormal basis $\gamma$ for V such that the first k columns of $[U]_{\gamma}$ form an orthonormal set
2 answers
2 votes
119 views
1 bookmarks
Partial differential equation about existence of limit
1 answers
2 votes
71 views
Rudin inverse function theorem interpretation
0 answers
2 votes
44 views
Outer measure definition how to understand intuitively
0 answers
2 votes
89 views
unitary operator and existence of $T=U^2$
1 answers
2 votes
27 views
existence of a PDE problem
2 answers
2 votes
260 views
Let $T: V \rightarrow W$ and $S: W \rightarrow Z$ be linear maps. If $S\circ T$ is an isomorphism, are $S$ and $T$ isomorphisms?
1 answers
2 votes
70 views
Explanation of Rudin's proof on change of variable
2 answers
2 votes
190 views
1 bookmarks
About definition of convex from Rudin's analysis
0 answers
2 votes
395 views
Characteristic polynomial splits problem
1 answers
2 votes
27 views
finding mean of mixed type CDF
0 answers
2 votes
28 views
Bivariate distribution joint PMF problem
1 answers
2 votes
189 views
Want the general idea of how proof works (Prove that $V=R(T^k) \oplus N(T^k)$ for some positive integer k.)
1 answers
2 votes
348 views
prove: For any finite-dimension vector space $V$ with ordered basis $\beta$, $\phi_\beta$ is an isomorphism.
1 answers
2 votes
558 views
Finding $c,b$ which minimizes $E(|X-c|)$ and $E[(X-b)^2]$
1 answers
2 votes
358 views
Let $u$ and $v$ be distinct vectors of a vector space $V$. Show that if {$u$,$v$} is a basis for $V$ and $a$ and $b$
1 answers
2 votes
415 views
An urn contains two red balls and four white balls. Sample successively five times at random and with replacement, so that the trials are independent.
1 answers
2 votes
278 views
Solve the initial value problem $xy'=y(xy-1), y(e^{-1})=e$
2 answers
2 votes
484 views
how does $(A \cap B) \cap (B \cap C)$ lead to $A \cap B \cap C$?
2 answers
1 votes
259 views
If W is a subspace of V and $x \notin W$, prove that there exists $f \in W^0$ such that $f(x) \neq 0$.
1 answers
1 votes
87 views
1 bookmarks
Prove that for any $x \in R$ and $t \geq 0$, $\inf_{x \in R} \phi(x) \leq u(x,t) \leq \sup_{x \in R} \phi(x)$
1 answers
1 votes
151 views
Heat equation proof
2 answers
1 votes
116 views
If two matrices have the same characteristic polynomial, they need not be unitarily equivalent. Why?
1 answers
1 votes
47 views
A metric space is separable if it contains a countable dense subset. Show that $R^k$ is separable.
1 answers
1 votes
60 views
deduce that there exists a unique polynomial q(x) of degree at most n such that$ q(c_i)=a_i$ for $0 \leq i \leq n$.
1 answers
1 votes
37 views
About a theorem of dual space