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3. (20 points) A symmetric real matrix A is positive definite (PD) if and only if r Ar > 0 for every vector r #
3. (20 points) A symmetric real matrix A is positive definite (PD) if and only if r Ar > 0 for every vector r # 0. Using this definition to determine whether or not a matrix is positive definite is however difficult. An alternative strategy is to use Sylvester's criterion, which states that a symmetric matrix is PD if and only if all its upper-left sub-matrices have a positive determinant
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