tag:blogger.com,1999:blog-7253035777210911687.post3001745943058535009..comments2016-10-20T22:01:43.436-07:00Comments on Mathematica bits: Visualizing SDP coneYaroslav Bulatovhttp://www.blogger.com/profile/06139256691290554110noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7253035777210911687.post-7203542242834290382014-10-04T11:21:50.644-07:002014-10-04T11:21:50.644-07:00These tips are really tremendous. Thank you for sh...These tips are really tremendous. Thank you for sharing with us. I think these tips are really effective for all in real estate dealing. <br /><a title="Mathematica" href="http://www.software-corner.ch/en/" rel="nofollow">Mathematica</a>mrhery124https://www.blogger.com/profile/11938811272570831174noreply@blogger.comtag:blogger.com,1999:blog-7253035777210911687.post-2999271232047765932012-02-02T12:42:07.375-08:002012-02-02T12:42:07.375-08:00Thanks for the prompt and thorough response!Thanks for the prompt and thorough response!Justinhttps://www.blogger.com/profile/04789687387824018809noreply@blogger.comtag:blogger.com,1999:blog-7253035777210911687.post-90460287355177798592012-01-31T22:57:14.779-08:002012-01-31T22:57:14.779-08:00Adding identity matrix is simply there to center t...Adding identity matrix is simply there to center the region since I wanted the point 0,0 to be feasible. I should've said symmetric PSD matrices. For symmetric 4x4 matrices, there an orthonormal basis that can be indexed by coordinates x1,...,x10 and I'm finding orthonormal pair of vectors in that coordinate space. So the matrices are orthogonal if you take inner product corresponding to the space of symmetric matricesYaroslav Bulatovhttps://www.blogger.com/profile/06139256691290554110noreply@blogger.comtag:blogger.com,1999:blog-7253035777210911687.post-71837197303969727192012-01-31T14:15:37.992-08:002012-01-31T14:15:37.992-08:00Very cool! I have a couple questions:
1. Why do y...Very cool! I have a couple questions:<br /><br />1. Why do you add the identity matrix when defining mat2? Doesn't that make a matrix whose eigenvalues are too big (each too big by 1)?<br /><br />2. In what sense are the two matrices in proj orthogonal? I see that the two vectors that Orthogonalize generates are orthogonal in the standard dot-product sense for vectors, but I would think that for the cone of positive semidefinite matrices, you would want two matrices Y and Z such that<br />Trace[ Transpose[Y] . Z ] == 0.<br />It's not clear to me that the two matrices in proj satisfy that. <br /><br />Thanks for the great blog! I'm learning a lot about convex optimization and Mathematica.Justinhttps://www.blogger.com/profile/04789687387824018809noreply@blogger.com