Rank-1 matrix as a product of rank-1 constriant and PSD check! [closed]

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Why a rank 1 matrix $W=xx^T$ can be written in the form of two following constraints?



$W=xx^T Longleftrightarrow (Wsucceq 0$ and $rank(W) = 1)
$










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closed as off-topic by Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did Sep 11 at 13:17


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Are you asking why $xx^T$ is positive semidefinite of rank $1$? Or are you asking why a positive semidefinite (symmetric) matrix of rank $1$ may be written as $xx^T$ for some vector $x$? Or both?
    – Arthur
    Sep 5 at 8:53















up vote
-3
down vote

favorite












Why a rank 1 matrix $W=xx^T$ can be written in the form of two following constraints?



$W=xx^T Longleftrightarrow (Wsucceq 0$ and $rank(W) = 1)
$










share|cite|improve this question













closed as off-topic by Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did Sep 11 at 13:17


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Are you asking why $xx^T$ is positive semidefinite of rank $1$? Or are you asking why a positive semidefinite (symmetric) matrix of rank $1$ may be written as $xx^T$ for some vector $x$? Or both?
    – Arthur
    Sep 5 at 8:53













up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











Why a rank 1 matrix $W=xx^T$ can be written in the form of two following constraints?



$W=xx^T Longleftrightarrow (Wsucceq 0$ and $rank(W) = 1)
$










share|cite|improve this question













Why a rank 1 matrix $W=xx^T$ can be written in the form of two following constraints?



$W=xx^T Longleftrightarrow (Wsucceq 0$ and $rank(W) = 1)
$







convex-optimization matrix-rank






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asked Sep 5 at 8:49









Muhammad Usman

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closed as off-topic by Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did Sep 11 at 13:17


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did Sep 11 at 13:17


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brian Borchers, Jendrik Stelzner, user21820, Arnaud D., Did
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Are you asking why $xx^T$ is positive semidefinite of rank $1$? Or are you asking why a positive semidefinite (symmetric) matrix of rank $1$ may be written as $xx^T$ for some vector $x$? Or both?
    – Arthur
    Sep 5 at 8:53

















  • Are you asking why $xx^T$ is positive semidefinite of rank $1$? Or are you asking why a positive semidefinite (symmetric) matrix of rank $1$ may be written as $xx^T$ for some vector $x$? Or both?
    – Arthur
    Sep 5 at 8:53
















Are you asking why $xx^T$ is positive semidefinite of rank $1$? Or are you asking why a positive semidefinite (symmetric) matrix of rank $1$ may be written as $xx^T$ for some vector $x$? Or both?
– Arthur
Sep 5 at 8:53





Are you asking why $xx^T$ is positive semidefinite of rank $1$? Or are you asking why a positive semidefinite (symmetric) matrix of rank $1$ may be written as $xx^T$ for some vector $x$? Or both?
– Arthur
Sep 5 at 8:53
















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