For which values of the constants p and q is the matrix
positive definite? (B has p’s on the diagonal and q’s elsewhere.) Hint: Exercise 8.1.17 is helpful.
Consider the following matrix with the constants p and q:
The eigen values of the following matrix B are p-q (multiplicity n-1) and nq+p-q, respectively (multiplicity 1). Because all eigen values must be positive for matrix B to be positive definite, we have:
As a result, we receive
As a result, the matrix B is positive definite for these values of the constants p and q.
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