Too much matrix inverse error?

New to Julia
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1

I use the inv() to do the inverse of the matrix, but I find that I don’t get the inverse matrix, or is it due to too much error?

This is my matrix

image
image1344×880 26.8 KB
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but inv(M1)*M1 not equal to unit matrix,
image
image1331×881 23.7 KB

Why is it happen?

2

Are you sure you really want the inverse matrix and not the solution of the equations which would be y \ M.

Also your matrix looks very sparse, maybe try to call explicitly

julia> using SparseArrays

julia> sparse(zeros((4,4)))
4×4 SparseMatrixCSC{Float64, Int64} with 0 stored entries:
  ⋅    ⋅    ⋅    ⋅ 
  ⋅    ⋅    ⋅    ⋅ 
  ⋅    ⋅    ⋅    ⋅ 
  ⋅    ⋅    ⋅    ⋅
2 Likes
3

Maybe your matrix is badly conditioned (i.e., nearly singular), in which case floating-point roundoff errors are enormously amplified when you try to invert the matrix. Try computing cond(M1) to get the condition number — probably it is huge (\sim 10^{15}).

If you are solving systems with an ill-conditioned matrix, you probably need to think carefully about what you are doing. (e.g. if you need a regularization, or if the problem is exactly singular and there is some other aspect of your problem that indicates which solution you want.)

6 Likes
4

You shouldn’t be inverting matrices. It’s not as bad as numerical algebra courses will tell you (as I fairly recently learned on here), but it’s still very rarely the best way to achieve what you want.