作业帮用MATLAB将二次型转换成标准二次型
来源：学生作业帮 编辑：作业帮 分类：综合作业 时间：2024/10/01 09:29:09
用MATLAB将二次型转换成标准二次型
将二次型f（X1,X2,X3）=4*X1^2+11*X1*X2+4*X2^2+11*X2*X3+4X3^2+11*X3*X4+4*X4^2+11*X4*X5+4*X5^2用MATLAB转化标准二次型.
将二次型f（X1,X2,X3）=4*X1^2+11*X1*X2+4*X2^2+11*X2*X3+4X3^2+11*X3*X4+4*X4^2+11*X4*X5+4*X5^2用MATLAB转化标准二次型.
A=[4 11/2 0 0 0;11/2 4 11/2 0 0;0 11/2 4 11/2 0; 0 0 11/2 4 11/2; 0 0 0 11/2 4 ]
A =
4.0000 5.5000 0 0 0
5.5000 4.0000 5.5000 0 0
0 5.5000 4.0000 5.5000 0
0 0 5.5000 4.0000 5.5000
0 0 0 5.5000 4.0000
>> [P,D] = schur(A)
P =
0.2887 -0.5000 0.5774 0.5000 -0.2887
-0.5000 0.5000 -0.0000 0.5000 -0.5000
0.5774 -0.0000 -0.5774 -0.0000 -0.5774
-0.5000 -0.5000 0.0000 -0.5000 -0.5000
0.2887 0.5000 0.5774 -0.5000 -0.2887
D =
-5.5263 0 0 0 0
0 -1.5000 0 0 0
0 0 4.0000 0 0
0 0 0 9.5000 0
0 0 0 0 13.5263
A =
4.0000 5.5000 0 0 0
5.5000 4.0000 5.5000 0 0
0 5.5000 4.0000 5.5000 0
0 0 5.5000 4.0000 5.5000
0 0 0 5.5000 4.0000
>> [P,D] = schur(A)
P =
0.2887 -0.5000 0.5774 0.5000 -0.2887
-0.5000 0.5000 -0.0000 0.5000 -0.5000
0.5774 -0.0000 -0.5774 -0.0000 -0.5774
-0.5000 -0.5000 0.0000 -0.5000 -0.5000
0.2887 0.5000 0.5774 -0.5000 -0.2887
D =
-5.5263 0 0 0 0
0 -1.5000 0 0 0
0 0 4.0000 0 0
0 0 0 9.5000 0
0 0 0 0 13.5263