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What is the necessary condition for a real symmetric matrix $ A_{m\times m} $ to be written as $B*B^T$ where $B$ is an $(m\times 1)$ matrix ?

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    How about the more general case $A=B*C$ where $C$ is a $1\times m$ matrix and $A$ is a general matrix ?2012-06-02

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I'll answer the question from OP's comment:

How about the more general case $A=B∗C$ where $C$ is a $1×m$ matrix and $A$ is a general matrix ?

Take $A={\vec B}^T\vec C+{\vec C}^T\vec B$. Then $A$ is symmetric, due to $ A^T=\left({\vec B}^T\vec C+{\vec C}^T\vec B\right)^T=\left({\vec B}^T\vec C\right)^T+\left({\vec C}^T\vec B\right)^T={\vec C}^T\vec B+{\vec B}^T\vec C=A $