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Bookmark or Share- Why is the volume of a cone one third of the volume of a cylinder?$\begingroup$ another twist on this: The other well-known calculus way to find the volume of the cone is to integrate over the disks that make up the cross sectional areas, as you go from the base at 0 to the top at h.
- matrices - Why $a^H\text {diag} (bb^H)a=b^H\text {diag} (aa^H)b, a, b ...Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
- Can $\\lim_{h\\to 0}\\frac{b^h - 1}{h}$ be solved without circular ...In many places I have read that $$\lim_{h\to 0}\frac{b^h - 1}{h}$$ is by definition $\ln(b)$. Does that mean that this is unsolvable without using that fact or a related/derived one? I can of course solve it with L'Hospitals rule, but that uses the derivative of the exponential function which is exactly what I want to derive by solving this limit.
- Is B(H) a Hilbert space? - Mathematics Stack ExchangeThus, you get a proper subspace $\mathcal{HS}(H) \subsetneq B(H)$ consisting of Hilbert–Schmidt operators (that is, operators with finite Hilbert–Schmidt norm). The inner product can be given by $\langle A, B\rangle = \text{tr}(B^*A)$, where you have to prove first that the product of two Hilbert–Schmidt operators is a trace class operator.
- linear algebra - Let that $T \in \mathcal{B}(H)$ where H is a Hilbert ...Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
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