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AFA = 4 H |
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AGA = 4 G + 12 H |
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AHA = 4 F + 6 G + 9 H |
M | M' | M + M' | M + M' est bien
une matrice symétrique S2 est stable pour + |
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a | b | + | a' | b' | = | a + a' | b + b' | |
b | c | b' | c' | b + b' | c + c' |
k | M | k M | k M est bien
une matrice symétrique S2 est stable pour . |
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k | a | b | = | k a | k b | |
b | c | k b | k c |
u(F) | u(G) | u(H) | |
0 | 0 | 4 | F |
0 | 4 | 6 | G |
4 | 12 | 9 | H |
4 | x | + | 0 | y | + | 4 | z | = | 0 | => x = −z | |
0 | x | + | 8 | y | + | 6 | z | = | 0 | => y = −(3/4) z | |
4 | x | + | 12 | y | + | 13 | z | = | 0 | => −4 z − 9 z + 13 z = 0 z = 0 |
−1 | x | + | 0 | y | + | 4 | z | = | 0 | => x = 4 z | |
0 | x | + | 3 | y | + | 6 | z | = | 0 | => y = −2 z | |
4 | x | + | 12 | y | + | 8 | z | = | 0 | => 16 z − 24 z + 8 z = 0 z = 0 |
−16 | x | + | 0 | y | + | 4 | z | = | 0 | => x = (1/4) z | |
0 | x | + | −12 | y | + | 6 | z | = | 0 | => y = (1/2) z | |
4 | x | + | 12 | y | + | −7 | z | = | 0 | => z + 6 z − 7 z = 0 z = 0 |
V−4 | V1 | V16 | u(V−4) | u(V1) | u(V16) | ||||
P = | 4 | 4 | 1 | F | D = | −4 | 0 | 0 | V−4 |
3 | −2 | 2 | G | 0 | 1 | 0 | V1 | ||
−4 | 1 | 4 | H | 0 | 0 | 16 | V16 |
D + 4 I | D − I | D − 16 I | ||||||||||||
0 | 0 | 0 | × | −5 | 0 | 0 | × | −20 | 0 | 0 | = | 0 | 0 | 0 |
0 | 5 | 0 | 0 | 0 | 0 | 0 | −15 | 0 | 0 | 0 | 0 | |||
0 | 0 | 20 | 0 | 0 | 15 | 0 | 0 | 0 | 0 | 0 | 0 |