All Questions
7 questions with no upvoted or accepted answers
3
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489
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Generalization of Carleman coefficients to multivariable functions - Carleman tensor?
Recently I learned about a matrix called
Carleman matrix. It is a matrix used to represent function iteration with matrix multiplying.
Carleman linearization is a technique used to embed a finite
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2
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77
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Rank-1 decomposability of symmetric tensors
My question is about rank-1 decomposability of symmetric tensors over the reals.
Let $v_1,\dots,v_n\in\mathbb{R}^d$ be vectors. Construct the object:
$$
V=\sum_{j=1}^n \underbrace{v_j\otimes v_j\...
- 1,096
1
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0
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155
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Some kind of product of two 2d tensors to create a 3d tensor?
I recently need to apply the following concept of product of two 2d tensors to create a 3d tensor (tensors understood as generalized arrays):
given two 2d tensors $A_{m\times n}$ and $B_{n\times p}$, ...
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1
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140
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Adjacency matrix/tensor operations for graph sequences?
Consider a graph $G=(V,E)$. Its adjacency matrix $A$ is defined by $A_{u,v} = 1$ if $(u,v)\in E$, $0$ otherwise.
Consider a vector $x$ that associates a value $x_v$ to each vertex of $G$. Consider the ...
- 1,444
1
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305
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tensor/hypermatrix analogues of $GL(n,\mathbb{C})$?
Please excuse me if this question turns out to be incredibly silly for one reason or another.
Are there tensor/hypermatrix analogues of $GL(n,\mathbb{C})$ that are interesting? What I'm mainly ...
- 1,075
0
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133
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A question from Richard Hamilton's paper "A matrix Harnack estimate for the heat equation"
Richard Hamilton "A matrix Harnack estimate for the heat equation. Communications in Analysis and Geometry. 1(1993), 113-126."
On page 125, at the end of the proof of Theorem 4.3, I abstract ...
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Is the kernel $\vert d_X - d_Y \vert^p$ conditionally negative definite?
Given two finite metric spaces $(X,d_X)$ and $(Y,d_Y)$, for $p > 0$, define the kernel ($4$-D tensor) $K$ on $(X \times Y)^2$ by:
$$K\big( (x_i, y_k), (x_j, y_l) \big) = \vert d_X(x_i, x_j) - d_Y(...
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