Why is the inverse of a symmetric matrix not symmetric?!

18 次查看（过去 30 天）
Ted
Ted 2013-5-8
Hi all, As far as I know, the inverse of symmetric matrix is always symmetric. However, I have a symmetric covariance matrix, call it C, and when I invert it (below), the solution, invC, is not symmetric!
>> invC = inv(C); % (inefficient I know, but it should still work...)
>> isequal(invC,invC')
ans = 0
Has anyone had this issue? Can this be due to rounding errors? My matrix is 1810x1810 with many entries like 0.0055, etc.
Thanks in advance!

请先登录，再回答此问题。

采纳的回答

Roger Stafford
Roger Stafford 2013-5-8
Yes, it's roundoff error. Instead of 'isequal' which demands exact equality, try displaying the difference invC-invC' to see if the differences fall within the range of what you would regard as reasonable round off errors. With a matrix which is close to being singular these can be surprisingly large sometimes.
  2 个评论
Ted
Ted 2013-5-10
Thanks for the tip.
The errors were small. I've now forced my "inverse" to be symmetric:
>> invCtrans = invC';
>> invC = triu(invC) + tril(invCtrans) - diag(diag(invC);
What I'm really trying to do now is use the chol() command for cholesky factorization. I know I need a symmetric positive definite matrix (spd), and I've checked by using eigs(invC,10,0), which tells me the 10 smallest eigenvalues are all positive. I'm still getting the following though:
>> U = chol(invC)
error using chol: matrix must be positive definite
... Any thoughts? Doesn't my eigenvalues test show that invC is spd?
Ted
Ted 2013-5-10
Never mind. I was getting the 10 eigenvalues with smallest magnitude, rather than the "most-negative."

请先登录，再进行评论。

更多回答（1 个）

Youssef Khmou
Youssef Khmou 2013-5-8
编辑：Youssef Khmou 2013-5-8
hi,
Try to use a tolerance criterion :
C=symdec(100,100);
C=C/max(C(:))
I1=inv(C);
I2=inv(C');
norm(I1-I2) % its not zeros but saturated to zero (1e-n , n>20 )

类别

在 Help Center 和 File Exchange 中查找有关 Linear Algebra 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by