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Nov
25
answered Efficient inversion of a symmetric, positive definite matrix
Nov
19
answered Prove $ A^-=\dfrac{1}{4}(-A^2+4A+I)$
Nov
19
revised show that $\mathsf E(Y|X)=\mu_2+\rho\dfrac{\sigma_2}{\sigma_1}(X-\mu_1)$
edited body
Nov
19
answered show that $\mathsf E(Y|X)=\mu_2+\rho\dfrac{\sigma_2}{\sigma_1}(X-\mu_1)$
Nov
17
revised Can product of two singular matrices be invertible?
The implications go both ways
Nov
17
suggested approved edit on Can product of two singular matrices be invertible?
Nov
15
comment Jensen’s inequality
@Did Then hopefully the wikipedia link is sufficiently helpful.
Nov
15
revised Jensen’s inequality
edited body
Nov
15
answered Jensen’s inequality
Nov
14
awarded  Civic Duty
Nov
14
comment Eigenvalues of a sum of rank-one matrices?
This is excellent!
Nov
11
answered Why is this nested sum formula true
Nov
8
comment Counterexample for $\| (\Phi^\top \Xi \Phi)^\dagger \Phi^\top \Xi P \Phi \|_2 \leq 1$
Are they no conditions on phi like norm phi <= 1?
Oct
27
revised Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
added 25 characters in body
Oct
27
comment Limit of $n(a^{1/n}-1)$ as $n \to \infty$
You mean $(e^x - 1)/x$. Also as n tends to infinity, x tends to 0.
Oct
27
revised Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
added 1 character in body
Oct
27
comment Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
Now, I have rewritten the answer somewhat differently and hopefully, the derivation is a bit more clearer now.
Oct
27
revised Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
added 1354 characters in body
Oct
27
comment Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
I didn't replace $\cos^{n+1}$ with $\cos^{2k}$. I replaced it with $\cos^{2k+2}$. I just wrote the formula for general even powers. For (a) and (b), I have updated the answer with details on how to prove them, they are quite simple to prove.
Oct
27
revised Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
added 367 characters in body