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Unexpected result calculating the determinant of a singular matrix (42S)
10-23-2019, 11:06 PM
Post: #26
RE: Unexpected result calculating the determinant of a singular matrix (42S)
Hi, Werner:

(10-23-2019 07:01 AM)Werner Wrote:  
(10-23-2019 04:50 AM)Valentin Albillo Wrote:  But try instead with AM#7, a matrix of the same dimensions (7x7) and similarly-sized integer elements, as detailed in my article

Mean Matrices
, under "Can it get any worse ?"

Still works..

Ok, I give up.

Quote:A 7x7 matrix with integer elements less than 100 and determinant 1 will always have at least 1 digit correct when the calculations are done with 15 digits

I can't try and find a counterexample to what you state because I don't have an HP48-whatever to check if my attempts work or not so I'll take your word for it.

Quote:Now, Valentin, I have always wondered how you created these matrices, and I've asked you once before (a very long time ago, admittedly). Can you shed some light on this?

I don't remember you asking me about this but you're right, it's been an awfully long time since then. As for shedding some light, it's complicated to honor your request because I recently suffered a couple of computer disasters in quick succession and haven't still fully recovered from them, right now my main computing device is a tablet.

One of the machines which suddenly died had the indexes to all my materials in the many external HDD drives I own which hold my archived materials, so to say, and thus makes it extremely difficult to find old, archived files without looking through them all, many terabytes.

From memory (and it's been a looooong time) I think I started from a number of suitable matrices (i.e., low dimensions, say 7x7, small integer elements, determinant 1) and defined a series of matrix manipulations that would preserve the determinant of the matrices being created anew by the process. Then I created a program which (1) performed the determinant-preserving manipulations, (2) implemented a genetic-like algorithm that created new generations of matrices and selected the best ones according to some criteria, and (3) after letting it run for a long while it would finally output the best matrices found.

The process could be either fully automatic, running unattended, or I could use it interactively and somewhat direct "evolution" to the most promising branches.

Sorry for the vagueness but I don't recall many details right now. I remember that the program was mid-sized and moderately complex and it finally produced a number of 7x7 AM matrices, from #1 to #7, as well as some others of various dimensions and element sizes.


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RE: Unexpected result calculating the determinant of a singular matrix (42S) - Valentin Albillo - 10-23-2019 11:06 PM

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