The symmetric factorization A = LDLT means that x TAx = x TLDLT x: h x yi " a b b c#"x y
Chapter 6, Problem 6.2.29(choose chapter or problem)
The symmetric factorization A = LDLT means that x TAx = x TLDLT x: h x yi " a b b c#"x y # = h x yi " 1 0 b/a 1 #"a 0 0 (acb 2 )/a #"1 b/a 0 1 #"x y # . The left-hand side is ax2 +2bxy+cy2 . The right-hand side is a(x + b a y) 2 + y 2 . The second pivot completes the square! Test with a = 2, b = 4, c = 10.
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