rank of a resultant matrix

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If I multiply a rank one symmetric positive semidefinite matrix with a diagonal matrix(diagonal matrices are full rank), both matrices have the same dimensions. Can I say/predict anything about the rank of the resultant matrix?



Thanks.




matrix-rank




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  • 1




    Yes, it will be at most a rank one matrix. In general, given two matrices $A,B$, you have $textrank(AB) le mintextrank(A),textrank(B)$. So, if one of the matrices has rank 1, that is the upper bound for the rank of the product of the two matrices.
    – InterstellarProbe
    Jul 31 at 18:39











  • @InterstellarProbe The diagonal matrix is known to be full rank.
    – amd
    Jul 31 at 19:51










  • @amd I gave one piece of information to get the OP started. I did not post it as an answer because it is not a complete answer. I was just hoping it would help the OP figure it out on his/her own. While the diagonal matrix is known to be full rank, the other is rank one.
    – InterstellarProbe
    Jul 31 at 20:27















up vote
-4
down vote

favorite












If I multiply a rank one symmetric positive semidefinite matrix with a diagonal matrix(diagonal matrices are full rank), both matrices have the same dimensions. Can I say/predict anything about the rank of the resultant matrix?



Thanks.




matrix-rank




share|cite|improve this question















  • 1




    Yes, it will be at most a rank one matrix. In general, given two matrices $A,B$, you have $textrank(AB) le mintextrank(A),textrank(B)$. So, if one of the matrices has rank 1, that is the upper bound for the rank of the product of the two matrices.
    – InterstellarProbe
    Jul 31 at 18:39











  • @InterstellarProbe The diagonal matrix is known to be full rank.
    – amd
    Jul 31 at 19:51










  • @amd I gave one piece of information to get the OP started. I did not post it as an answer because it is not a complete answer. I was just hoping it would help the OP figure it out on his/her own. While the diagonal matrix is known to be full rank, the other is rank one.
    – InterstellarProbe
    Jul 31 at 20:27













up vote
-4
down vote

favorite









up vote
-4
down vote

favorite











If I multiply a rank one symmetric positive semidefinite matrix with a diagonal matrix(diagonal matrices are full rank), both matrices have the same dimensions. Can I say/predict anything about the rank of the resultant matrix?



Thanks.




matrix-rank




share|cite|improve this question











If I multiply a rank one symmetric positive semidefinite matrix with a diagonal matrix(diagonal matrices are full rank), both matrices have the same dimensions. Can I say/predict anything about the rank of the resultant matrix?



Thanks.





matrix-rank





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 31 at 18:19









Adil

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  • 1




    Yes, it will be at most a rank one matrix. In general, given two matrices $A,B$, you have $textrank(AB) le mintextrank(A),textrank(B)$. So, if one of the matrices has rank 1, that is the upper bound for the rank of the product of the two matrices.
    – InterstellarProbe
    Jul 31 at 18:39











  • @InterstellarProbe The diagonal matrix is known to be full rank.
    – amd
    Jul 31 at 19:51










  • @amd I gave one piece of information to get the OP started. I did not post it as an answer because it is not a complete answer. I was just hoping it would help the OP figure it out on his/her own. While the diagonal matrix is known to be full rank, the other is rank one.
    – InterstellarProbe
    Jul 31 at 20:27













  • 1




    Yes, it will be at most a rank one matrix. In general, given two matrices $A,B$, you have $textrank(AB) le mintextrank(A),textrank(B)$. So, if one of the matrices has rank 1, that is the upper bound for the rank of the product of the two matrices.
    – InterstellarProbe
    Jul 31 at 18:39











  • @InterstellarProbe The diagonal matrix is known to be full rank.
    – amd
    Jul 31 at 19:51










  • @amd I gave one piece of information to get the OP started. I did not post it as an answer because it is not a complete answer. I was just hoping it would help the OP figure it out on his/her own. While the diagonal matrix is known to be full rank, the other is rank one.
    – InterstellarProbe
    Jul 31 at 20:27








1




1




Yes, it will be at most a rank one matrix. In general, given two matrices $A,B$, you have $textrank(AB) le mintextrank(A),textrank(B)$. So, if one of the matrices has rank 1, that is the upper bound for the rank of the product of the two matrices.
– InterstellarProbe
Jul 31 at 18:39





Yes, it will be at most a rank one matrix. In general, given two matrices $A,B$, you have $textrank(AB) le mintextrank(A),textrank(B)$. So, if one of the matrices has rank 1, that is the upper bound for the rank of the product of the two matrices.
– InterstellarProbe
Jul 31 at 18:39













@InterstellarProbe The diagonal matrix is known to be full rank.
– amd
Jul 31 at 19:51




@InterstellarProbe The diagonal matrix is known to be full rank.
– amd
Jul 31 at 19:51












@amd I gave one piece of information to get the OP started. I did not post it as an answer because it is not a complete answer. I was just hoping it would help the OP figure it out on his/her own. While the diagonal matrix is known to be full rank, the other is rank one.
– InterstellarProbe
Jul 31 at 20:27





@amd I gave one piece of information to get the OP started. I did not post it as an answer because it is not a complete answer. I was just hoping it would help the OP figure it out on his/her own. While the diagonal matrix is known to be full rank, the other is rank one.
– InterstellarProbe
Jul 31 at 20:27
















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