equivalent definition of positive semidefinite matrix

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A matrix $M$ is positive semidefinite if and only if $y^T M y geq 0$ for all possible $y$.
We can also show that $M geq 0$ if and only if $[bary^T,1 ]M[bary^T,1]^T geq 0$ for all possible $bary$. That is we fix the last element of $y$ to be 1. This can be proved by the continuity of $ y rightarrow y^T M y$.



My question is: is this definition well-known? If so, what is the name of this definition?




optimization positive-semidefinite




share|cite|improve this question















  • 1




    It is not a definition.
    – copper.hat
    Aug 6 at 1:31










  • whatever you can call it a classification. Just want to find a reference to this trick.
    – Pew
    Aug 10 at 3:32










  • I don't think it has a name.
    – copper.hat
    Aug 10 at 3:42










  • Ok is this trick well-known? Do you know a reference or I just need to do the argument myself before using this trick?
    – Pew
    Aug 10 at 3:44










  • I think it would fall into the 'fairly clear in context' category. I don't have a reference.
    – copper.hat
    Aug 10 at 3:46















up vote
0
down vote

favorite












A matrix $M$ is positive semidefinite if and only if $y^T M y geq 0$ for all possible $y$.
We can also show that $M geq 0$ if and only if $[bary^T,1 ]M[bary^T,1]^T geq 0$ for all possible $bary$. That is we fix the last element of $y$ to be 1. This can be proved by the continuity of $ y rightarrow y^T M y$.



My question is: is this definition well-known? If so, what is the name of this definition?




optimization positive-semidefinite




share|cite|improve this question















  • 1




    It is not a definition.
    – copper.hat
    Aug 6 at 1:31










  • whatever you can call it a classification. Just want to find a reference to this trick.
    – Pew
    Aug 10 at 3:32










  • I don't think it has a name.
    – copper.hat
    Aug 10 at 3:42










  • Ok is this trick well-known? Do you know a reference or I just need to do the argument myself before using this trick?
    – Pew
    Aug 10 at 3:44










  • I think it would fall into the 'fairly clear in context' category. I don't have a reference.
    – copper.hat
    Aug 10 at 3:46













up vote
0
down vote

favorite









up vote
0
down vote

favorite











A matrix $M$ is positive semidefinite if and only if $y^T M y geq 0$ for all possible $y$.
We can also show that $M geq 0$ if and only if $[bary^T,1 ]M[bary^T,1]^T geq 0$ for all possible $bary$. That is we fix the last element of $y$ to be 1. This can be proved by the continuity of $ y rightarrow y^T M y$.



My question is: is this definition well-known? If so, what is the name of this definition?




optimization positive-semidefinite




share|cite|improve this question











A matrix $M$ is positive semidefinite if and only if $y^T M y geq 0$ for all possible $y$.
We can also show that $M geq 0$ if and only if $[bary^T,1 ]M[bary^T,1]^T geq 0$ for all possible $bary$. That is we fix the last element of $y$ to be 1. This can be proved by the continuity of $ y rightarrow y^T M y$.



My question is: is this definition well-known? If so, what is the name of this definition?





optimization positive-semidefinite





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 6 at 1:14









Pew

296114




296114







  • 1




    It is not a definition.
    – copper.hat
    Aug 6 at 1:31










  • whatever you can call it a classification. Just want to find a reference to this trick.
    – Pew
    Aug 10 at 3:32










  • I don't think it has a name.
    – copper.hat
    Aug 10 at 3:42










  • Ok is this trick well-known? Do you know a reference or I just need to do the argument myself before using this trick?
    – Pew
    Aug 10 at 3:44










  • I think it would fall into the 'fairly clear in context' category. I don't have a reference.
    – copper.hat
    Aug 10 at 3:46













  • 1




    It is not a definition.
    – copper.hat
    Aug 6 at 1:31










  • whatever you can call it a classification. Just want to find a reference to this trick.
    – Pew
    Aug 10 at 3:32










  • I don't think it has a name.
    – copper.hat
    Aug 10 at 3:42










  • Ok is this trick well-known? Do you know a reference or I just need to do the argument myself before using this trick?
    – Pew
    Aug 10 at 3:44










  • I think it would fall into the 'fairly clear in context' category. I don't have a reference.
    – copper.hat
    Aug 10 at 3:46








1




1




It is not a definition.
– copper.hat
Aug 6 at 1:31




It is not a definition.
– copper.hat
Aug 6 at 1:31












whatever you can call it a classification. Just want to find a reference to this trick.
– Pew
Aug 10 at 3:32




whatever you can call it a classification. Just want to find a reference to this trick.
– Pew
Aug 10 at 3:32












I don't think it has a name.
– copper.hat
Aug 10 at 3:42




I don't think it has a name.
– copper.hat
Aug 10 at 3:42












Ok is this trick well-known? Do you know a reference or I just need to do the argument myself before using this trick?
– Pew
Aug 10 at 3:44




Ok is this trick well-known? Do you know a reference or I just need to do the argument myself before using this trick?
– Pew
Aug 10 at 3:44












I think it would fall into the 'fairly clear in context' category. I don't have a reference.
– copper.hat
Aug 10 at 3:46





I think it would fall into the 'fairly clear in context' category. I don't have a reference.
– copper.hat
Aug 10 at 3:46
















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