# Questions tagged [outer-product]

Given two vectors $\vec{u},\vec{v}$ of dimensions $m,n$ respectively, their outer product $\vec{u}\otimes \vec{v}$ is the $m\times n$ matrix $M$ with entries $m_{ij}=u_i v_j$.

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### If a matrix is an outer product of two vectors; can I determine the vectors? [closed]

I am working with floating point numbers. There is a 3x3 matrix that has determinant 1e-14. I have reason to believe this matrix is an outer product of two vectors. If the assumption is correct, how ...
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### Outer product of row vectors. Does $\mathbf{x}^T \otimes \mathbf{y}^T$ = $\mathbf{x} \otimes \mathbf{y}$?

Does $\mathbf{x}^T \otimes \mathbf{y}^T$ = $\mathbf{x} \otimes \mathbf{y}$?
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### Why can we substitute $V_{\mu \nu}$ to $V_{\mu ; \nu}$ while inducing contracted Bianchi identity?

After $( A_\mu B_\nu )_{; \sigma ; \rho} - ( A_\mu B_\nu )_{; \rho ; \sigma} = A_\alpha B_\nu R^\alpha_{\mu \rho \sigma} + A_\mu B_\alpha R^\alpha_{\nu \rho \sigma}$ where $A_\mu B_\nu$ is outer ...
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### Is there a counterpart to the outer product? I.e., divide every term of a vector by every other term of another vector.

Regarding the dyadic product (specifically, the outer product or tensor product), notated as $\otimes$, can you provide comment on its counterpart? I'm not sure if it has a name, or if it has matrix ...
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### What is the intuition behind the outer product of two eigenvectors?

I know that the outer product of every two eigenvector forms a 2-D basis for the 2-D matrices. For example, when we write a matrix based on its eigenvectos, we have:  X = \sum_{i,j} \lambda_{i,j}...
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