# Questions tagged [inner-products]

For questions about inner products and inner product spaces, including questions about the dot product.

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### Characterizing the dual lattice of an real vector space

Let $n\in\mathbf{N}$, $V=$ {$(x_1,...,x_n)\in\mathbf{R}^n|\sum\limits_{i=1}^n x_i=0$} be a real vector space, Let $l=V\cap\mathbf{Z}^n$ in $V$. Let $(\cdot,\cdot)$ be a restriction to $V$ of the ...
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1 vote
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### How axioms of inner product ensure that an instantiation/realization capture notion of angle correctly?

Axiomatic definition of inner product can lead to various instantiations like euclidean inner product or complex inner product or weighted inner product etc. Whatever the special case, we can be sure, ...
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### Show that function is positive definite

In the process of showing that the function$$\langle \mathbf{z}, \mathbf{w}\rangle=\overline{z_1}w_1+(1+i)\overline{z_1}w_2+(1-i)\overline{z_2}w_1+3\overline{z_2}w_2$$ is ...
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1 vote
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### Can one solve this complex linear equation

Suppose the equations are as follows: $$\text{tr}\{AH\}= c$$ where $c \in \mathbb{C}$ and $A$ is a symmetric matrix in $M_{N}(\mathbb{R})$ are both known and $H$ is a Hermitian matrix which looks like:...
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### Interpretation of $\max \sup$

I am reading the regret analysis proof of LinUCB given in Lattimore's Bandit Algorithms. He makes the following assumption:  \max\limits_{t\in[n]}\sup\limits_{a,b\in\mathcal{A}_t} \langle\theta^* , ...
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