Given the vector space $\mathbb{R}^n$, endowed with the standard inner (dot) product $\langle\cdot,\cdot\rangle:\mathbb{R}^n\times \mathbb{R}^n\to\mathbb{R}$, the problem of almost …

There are books or articles that deal with generalizations of functional analysis in the sense that the inner product need not be positive-definite or that works with functions ove …

Hello, I am en engineer working in radar research. I came accross a problem I cannot seem to find math literature on it. I can ask it in two different ways. Perhaps depending on …

Let $n,d_1,\ldots,d_n > 1$ be integers, and $V_1, \ldots, V_n$ be inner product spaces over $\mathbb C$, having dimensions $d_1, \ldots, d_n$ respectively. We consider the ways in …

This is an extended re-post of a question that I have asked on MSE not a long time ago. But anyway, it seems more appropriate for MO. To begin with, in a real inner product space …

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra and let $U_q(\mathfrak{g})$ be some incarnation of the quantized universal enveloping algebra of $\mathfrak{g} …

Background: I am a theoretical computer scientist (PhD candidate) and have done graduate level courses in Algebra. I want to understand the following theorem from the book "Symmet …

For Hermitian matrices and operators, the most "natural" inner product is $f^H \cdot g$ or $\int f^* g\; dx$. A similar situation holds interpreting Fourier transforms as the inner …

Dan Popescu asked me the following question, and since I'm not an expert I'm throwing his question on MO. Suppose that $A$ is a finite-dimensional vector space over an ordered fie …

I'm writing a linear algebra exam next week and it's come to my attention that the prof that designed the test uses a different convention for complex inner product than the one my …

Given $n$ hermitian (positive-semidefinite) operators $Q_1,\cdots,Q_n$ in finite dimensional Hilbert space (the dimension can be very large), is there a mapping $\phi$ maps $Q_i$ t …

Hi all, As a part of a research I'm working on (involving derandomization of linear threshold functions), I'm trying to understand the following problem: Is there a small (polyno …

I do not know if the following question makes sense. Is it possible to define an inner product (that gives real values) for vectors on a sphere $S^n$ (let say $S^1$)? The set of t …

So, if you talk to the right people, they will tell you that the braiding of the category of representations of a quantum group are not unitary and that one can fix this by taking …

I want to take the inverse of a dot product, where both vectors have complex components. In other words, if $\textbf{A} \cdot \textbf{B} = d$, and I know $\textbf{A}$ and $d$, I w …