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I'm looking for something similar to Kronecker's product that creates matrix based on two vectors I'm thinking about either:

$$ (1,2,3) @ (4,5,6) = \begin{bmatrix} (1, 4) & (2, 4) & (3, 4) \\[0.3em] (1, 5) & (2, 5) & (3, 5) \\[0.3em] (1, 6) & (2, 6) & (3, 6) \end{bmatrix} $$

or

$$ (1,2,3) @ (4,5,6) = \begin{bmatrix} 1 \cdot 4 & 2 \cdot 4 & 3 \cdot 4 \\[0.3em] 1 \cdot 5 & 2 \cdot 5 & 3 \cdot 5 \\[0.3em] 1 \cdot 6 & 2 \cdot 6 & 3 \cdot 6 \end{bmatrix} $$

where obviously @ is my imaginary operation.

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    If they were sets, though, then [Cartesian products](http://en.wikipedia.org/wiki/Cartesian_product#Basic_properties). Hmm I have no other idea.2012-08-22
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    $v\cdot w^t$?${}$2012-08-22
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    @tomasz for second one you're obviously right, I don't know how I missed that.2012-08-22

2 Answers 2

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The second one is sometimes called the outer product.

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I don't know why this question has a negative vote. If you have row vectors $u = (1,2,3)$ and $v = (4,5,6)$, the latter matrix is $v^Tu$. The former isn't really a matrix in the sense I know of, because its entries aren't numbers.

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    Well, the former is a matrix with entries in the ring $R^2$, where $R$ is the base ring of the vectors. I doubt there's any common way to denote such an operation, though. Doesn't seem very natural.2012-08-22
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    IIRC matrices are more versatile, and as long as entries belong to a ring that has some operations defined, they are valid.2012-08-22
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    @MarcinRaczkowski: Yes. I'm just saying that the operation $(R^{n\times 1})^2\to (R^2)^{n\times n}$ doesn't look natural.2012-08-22