Metoda Lui Fadeev T [PDF]
A = {{1, - 2, 8}, {2, - 1, - 1}, {3, - 1, 2}}; MatrixForm[A] A1 = A; k1 = - Tr[A1]; B1 = A1 + k1 * IdentityMatrix[3]; A2
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A = {{1, - 2, 8}, {2, - 1, - 1}, {3, - 1, 2}}; MatrixForm[A] A1 = A; k1 = - Tr[A1]; B1 = A1 + k1 * IdentityMatrix[3]; A2 = A.B1; k2 = - Tr[A2] 2; B2 = A2 + k2 * IdentityMatrix[3]; A3 = A.B2; k3 = - Tr[A3] 3; B3 = A3 + k3 * IdentityMatrix[3]; For[i = 1, i ≤ 3, i ++, lamda[i] = t /. Solve[1 * t ^ 3 + k1 * t ^ 2 + k2 * t + k3 == 0, t][[i]]; ]; lamda[1] lamda[2] lamda[3] R1 = lamda[1] ^ 2 * IdentityMatrix[3] + lamda[1] * B1 + B2; R2 = lamda[2] ^ 2 * IdentityMatrix[3] + lamda[2] * B1 + B2; R3 = lamda[3] ^ 2 * IdentityMatrix[3] + lamda[3] * B1 + B2; Print[N[MatrixForm[R1]], "
", N[MatrixForm[R2]], "
", N[MatrixForm[R3]]];
1 -2 8 2 -1 -1 3 -1 2 -1 1 2 1 2
3 -
85
3 +
85
- 1. - 2. 2. - 9. - 18. 18. - 2. - 4. 4.
1 -2 8 Det 2 - 1 - 1 3 -1 2 19
9.78046 2.21954 - 14.8782 - 13.2195 - 3. 20.1098 - 8.32932 - 1.89023 12.6707
28.2195 - 16.2195 58.8782 5.21954 - 3. 10.8902 19.3293 - 11.1098 40.3293