MATLAB: Svd prescision is very bad.

doubleepsMATLABmatrixsinglesvd

it appears to be that when i use SVD i loose prescision how can i avoid loosing prescision and use svd function?
[U,S,V]=svd(T);
T=U*S*V'
the first T Matrix and the second are not the same.
here a comparation of the matrix before svd and after:
>> T
T =
-0.4609 + 0.4970i   0.0023 + 0.0267i  -0.0267 + 0.0028i
 0.0023 + 0.0270i  -0.5192 - 0.4982i  -0.0023 - 0.0267i
-0.0267 + 0.0028i  -0.0023 - 0.0270i  -0.4609 + 0.4970i
>> [U,S,V]=svd(T); >> Tsvd=U*S*V'
Tsvd =
-0.4609 + 0.4970i   0.0023 + 0.0267i  -0.0267 + 0.0028i
 0.0023 + 0.0270i  -0.5192 - 0.4982i  -0.0023 - 0.0267i
-0.0267 + 0.0028i  -0.0023 - 0.0270i  -0.4609 + 0.4970i
>> difference=T-Tsvd
difference =
   1.0e-15 *
-0.0555 - 0.1110i   0.0247 - 0.0312i  -0.4025 + 0.3092i
-0.0278 - 0.0173i   0.0000 - 0.3331i  -0.0494 + 0.0555i
-0.0486 + 0.0867i   0.0694 + 0.1076i   0.0000 + 0.0555i

Best Answer

Please let us know how familiar your are with numerical mathematics. The effect you see here is to be expected, but I do not want to come across as too blunt just pointing you to
eps
I could find a document that describes a bit about the why.
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