0
$\begingroup$

I have a large matrix, around 10x10. Each individual element in the matrix itself is also a very large number, roughly of the order 10^30.

I know that matrices can be used to solve linear equations. So if there is an equation ax + by = c then can I denote the 10x10 matrix, a, using x&y which are just 2 real numbers and b&c which are matrices. Can this be used to compress the larger matrix?

If not, then is there any other way that I can use so that I can use some form of short expression which can be evaluated into the larger matrix?

  • 0
    For an arbitrary matrix, you can't compress it. Do you know any other information about the structure of the matrix? Could you perhaps post a sample matrix? (If you do, use Stack Exchange's code formatting: put 4 spaces at the start of each line of the matrix.)2012-10-21
  • 0
    There are many ways to generate large matrices from the small seed (like $n \times n$ identity matrix), but it is generally very hard to do it the opposite direction (i.e. from matrix generate a seed that could be later used to regenerate it) unless the matrix in question has very precisely defined structure (and even then it probably won't be easy). Good luck!2012-10-21
  • 1
    By the way, the theorem under section 9.2 of [the comp.compression FAQs](http://www.faqs.org/faqs/compression-faq/part1/section-8.html) justifies my first sentence. Don't be discouraged, though: if your matrix does have some further structure, you should be able to compress it.2012-10-21
  • 0
    apart from the dimensions of the matrix there is no other pattern in the structure. Perhaps I will find some luck converting the matrix into something else...2012-10-21
  • 1
    @ritratt: If there really is no pattern at all, then you won't be able to compress it. See that theorem I linked.2012-10-21

0 Answers 0