Let $A$ be a complex $n\times n$ matrix. Can we always find two vectors $a,b\in \mathbb C^n$ such that $A=a\otimes b^T$?
Decomposition of matrices
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linear-algebra
matrices
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4Have you tried it for, say, $n=2$? – 2012-11-06
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0It seems like you should write either $ab^T$ or $a \otimes b$ instead of $a \otimes b^T$. At least it looks that way here: http://en.wikipedia.org/wiki/Outer_product – 2012-11-06
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0On second thought, if you mean the Kronecker product, then it's OK, but it does look strange to find this $\otimes$ sign in such a simple vector-and-vector situation. – 2012-11-06
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2What's the rank of $ab^T$? – 2012-11-06