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location Melbourne, Australia
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I am a professional software engineer and a Math hon-ours student.


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accepted linear transformation of real symmetric square positive semi-definite matrix
Apr
14
comment linear transformation of real symmetric square positive semi-definite matrix
@MichaelGrant Wow i was not aware that eigenvalues only existed for square matrices. So would it be correct to conclude then that i could pick any $n \times n$ square psd matrix for $U$ use it as multiple on the left side of $V$ to get a value for $W$ which would be psd as desired. ofcourse both $V$ and $W$ are also $n \times n$ matrices.
Apr
14
comment linear transformation of real symmetric square positive semi-definite matrix
@MichaelGrant I wanted to thank you for your kindness and for taking an interest in my question. I have learned from this exchange. I am currently trying to dig up on if the two definitions of postive semidefinite matrices have the same or different implications. If they turn up to be the same then i would assume my hypothesis is ill-formed, unless p = n, as you have suggested.
Apr
14
comment linear transformation of real symmetric square positive semi-definite matrix
I think i am hoping for W to be a cross-covariance matrix. I never knew there was a special name for it. Thank you for pointing this out.
Apr
14
comment linear transformation of real symmetric square positive semi-definite matrix
I think there is some confusion about the definition of positive semidefinite matrices specially in case of real matrices. I was under the assumption a better definition of positive semi definite matrix is that all eigenvalues are greater than or equal to zero.
Apr
14
revised linear transformation of real symmetric square positive semi-definite matrix
deleted 10 characters in body
Apr
13
answered Suggest an Antique Math Book worth reading?
Apr
13
comment linear transformation of real symmetric square positive semi-definite matrix
@MichaelGrant The discussion about this does make me suspect that $W$ may not be symmetric if it is non-square.
Apr
13
comment linear transformation of real symmetric square positive semi-definite matrix
@MichaelGrant I could be wrong but i would like to clarify here. Firstly I am interested in semi-Positive definite matrices not strictly positive definite. Secondly it is well known condition that covariance matrices must be semi-positive definite matrices. As they are allowed to be non square i can only conclude from this that it is possible to have non-square semi-positive definite matrices. If i am in correct in my understanding then please elaborate why this is not possible.
Apr
13
comment linear transformation of real symmetric square positive semi-definite matrix
@MichaelGrant I am looking to try find an appropriate example for my claim. I think covariance matrices fit this category.
Apr
13
comment linear transformation of real symmetric square positive semi-definite matrix
@MichaelGrant I believe a non-square matrix can be symmetric semi-positive definite.