(a) If A = a b b c is Hermitian (complex b), find its pivots and determinant. (b)
Chapter 6, Problem 6.1.11(choose chapter or problem)
(a) If A = a b b c is Hermitian (complex b), find its pivots and determinant. (b) Complete the square for x HAx. Now x H = [x1 x2] can be complex a|x1| 2 +2Rebx1x2 +c|x2| 2 = a|x1 + (b/a)x2| 2 + |x2| 2 . (c) Show that a > 0 and ac > |b| 2 ensure that A is positive definite. (d) Are the matrices 1 1+i 1i 2 and 3 4+i 4i 6 positive definite?
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