Proving $E_\lambda(T)=E_{\lambda^{-1}}(T^{-1})$
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
143765
To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
98710
Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
118996
Prove that $T$ is an orthogonal projection
18379
Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
79794
Prove the time inversion formula is brownian motion
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
83279
How can I find such a $z$? (Injectivity of $T(z) = \lambda z + \mu\bar{z}$)
147705
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?