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The matrix cookbook (page 16) offers this amazing result: $$A − A(A + B)^{−1}A = B − B(A + B)^{−1}B$$ This seems to be too unbelievable to...
Asked on 12/15/2021
2 answerI am still stuck to the differential equation:$$r(r-1)partial_r^2f+partial_rf-left[ dfrac{rho^2r^3}{r-1}+l(l+1)-dfrac{3}{r} right]f=0$$ According to the author of this paper, the solution has the form $$f(r)=(r-1)^rho...
Asked on 12/15/2021
1 answerI am new with singular homologyThis is a fair but hard exercise for all of my classmate, we all feel dizzy after Imagine what really happen...
Asked on 12/15/2021
2 answerIn Murphy's book on $C^*$-algebras, it is claimed that f $B$ is a $C^*$-subalgebra of a $C^*$-algebra $A$, then $sigma_A(b) cup {0} = sigma_B(b)...
Asked on 12/15/2021
0 answer5.6. Fact. If G and H are matrices such that GH is defined, then for all n≥0, we have $D_n(GH)⊆D_n(G)D_n(H)$Proof: By considering exterior powers, we reduce to the...
Asked on 12/15/2021
0 answerI know that for a bipartite graph, the adjacency matrix can be written asbegin{align}A =begin{pmatrix}0_{rr} & B \ B^T & 0_{ss}end{pmatrix}.end{align}Let...
Asked on 12/15/2021 by Chao
0 answerI have the following formula, which I believe it's true since it works in Mathematica for all values of $N$ I have tried, but I don't know how to...
Asked on 12/15/2021
2 answerPostscript to the question below. In trying to learn from the answers below, all of which I am grateful for, I read a historical article on the...
Asked on 12/15/2021 by Lars Ericson
5 answerI have a black-box discrete probability distribution $mathbf{p}$ (I can only get samples from it), two items in the support: $sigma_1, sigma_2$, and a procedure which estimates the...
Asked on 12/15/2021
0 answerLet $m : mathbb R^{d} to mathbb K$ measurable and $A: operatorname{dom}(A) to L^{p}(mathbb R^{d})$ such that $Af(x)=m(x)f(x)$ and $operatorname{dom}(A):={f in L^{p}(mathbb R^{d}):mf in L^{p}(mathbb R^{d})}$....
Asked on 12/15/2021
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