Practice question · Select all that apply
Which are required for positive definiteness of a 2x2 symmetric matrix?
Hints
- The minor conditions and the eigenvalue condition are equivalent.
- A vanishing trace would force the eigenvalues to have opposite signs.
Show the answer
- B. (second principal minor positive)
- C. (first principal minor positive)
- D. Both eigenvalues are positive
Why
All three are equivalent conditions for positive definiteness. The trace being zero would mean the eigenvalues sum to zero, implying indefiniteness.
Practise Quadratic Forms
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