第5章: 行列のノルム (pdf)

43 5 5.1 2 5.1 {ai,j ∈ R1 }n i,j=1 n {xi}n i=1 2 f(x1, x2, . . . , xn) = n X i=1 n X j=1 ai,jxixj 2 n x = (x1, x2, . . . , xn)T B 2 f(x) = xT Bx 5.2 2 f(x) x 6= 0 • f(x) > 0 (positive definite) • f(x) ≥ 0 (positive semidefinite) • f(x) < 0 (negative definite) • f(x) ≤ 0 (negative semidefinite) 5.1 2 2 f(x) = xT Ax A Q = [q1|q2| . . . |qn] y = QT x f(y) = r X i=1 λiy2 i , (r = rankA ≤ n) 2 (real qu