# Tagged Questions

Let $T$ be a linear operator acting on a finite-dimensional real or complex vector space. As a direct consequence (or rather a particular case) of the Riesz-Thorin theorem, we have $$\|T\|_2 \le ... 1answer 154 views ### Constructing a continuous matrix valued function Given d<k. Let {\cal M}_{d\times k}(\mathbb{R}) denotes the set of all d\times k real matrices and suppose that H:\mathbb{R}^k\rightarrow {\cal M}_{d\times k}(\mathbb{R}) is a continuous ... 0answers 172 views ### Closed-form expressions for dual norms of real normed vector spaces Didn't get any biters over at MSE, so I figure this place might be more appropriate... Say that V is a finite-dimensional real normed vector space, where for some v \in V the norm is notated by ... 1answer 254 views ### Decomposing bilinear forms in Hilbert spaces You are given a complex Hilbert space H with two equivalent Hilbert space structures <,> and <,>'. Define <,>''=<,> + <,>' to be the sum of our two scalar ... 2answers 412 views ### How do you compute the dual norm of an induced norm on a subspace of a finite-dimensional Lp-normed vector space? Say you have a finite-dimensional vector space V with an L^p norm on it. In general, the norm induced on a subspace V_s of doesn't have to be another L^p norm, so the unit sphere in V_s ... 1answer 402 views ### Do real vectors attain matrix norms? I apologize if the following question ends up being too elementary for this website; I asked it on math.SE a week ago and it remains unanswered. Let A be an n \times n matrix with real entries ... 1answer 318 views ### Completely bounded maps on Mn The aim of this question is to collect nice maps on M_n(\mathbb{C}) with the following property: \phi_n:M_n(\mathbb{C})\rightarrow M_n(\mathbb{C}) with ||\phi||=1 and ... 2answers 271 views ### Analogue of an orthogonal subspace in a noneuclidian normed space This question is related to http://mathoverflow.net/questions/50600/an-existence-question-on-linear-map. If the answer to this question is yes, it would solve the abovementioned other MO question. We ... 1answer 435 views ### Is exp(rA) = (exp(A))^r for real r and A in a Banach space? Is e^{(rA)} = (e^{A})^r when r \in \mathbb{R} and A is an element of a Banach algebra? Clearly if n is an integer, then e^{(nA)} = e^{A+A \cdots +A} = e^{A}e^{A}\cdots e^{A} = (e^{A})^n, ... 1answer 953 views ### Banach-Mazur distance between \ell^p-norms Let E^n be the real or complex space of dimension n. If N and M are two norms over E^n, and if A is an endomorphism, then$$\|A\|^M_N:=\sup_{x\ne0}\frac{M(Ax)}{N(x)} is an operator norm ...
Let $f:[n]\times [n] \rightarrow [0,1]$ be a function from pair of integers to the real interval [0.1]. I would like to find sets of complex vectors $X= \{x_i\}$ and $Y=\{y_j\}$ satisfying \$x_i\cdot ...