If a matrix is sensitive to roundoff errors, the computed value of its determinant may differ drastically from the exact value. For an example of this, set
U = round(100 ∗ rand(10));
U = triu(U, 1) + 0.1 ∗ eye(10)
In theory,
det(U) = det(UT ) = 10−10
and
det(UUT ) = det(U) det(UT ) = 10−20
Compute det(U), det(U’), and det(U ∗ U’ ) with MATLAB. Do the computed values match the theoretical values?
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