已知矩阵为100x100的矩阵，矩阵元素满足1/（i-j+0.4）,运用MATLAB求出矩阵特征根

Question

如题所述

Answer 1

解：先生成所需矩阵，100阶方阵，再用命令eig()求出特征根即可。

MATLAB的M文件如下：
A=[];
for i=1:100
for j=1:100
A(i,j)=1./(i-j+0.4);
end
end
A%显示所需的矩阵
eig(A)%计算出所有100个特征要
运行结果如下：
矩阵A略。
特征根
ans =
1.1252 + 3.0901i
1.1252 - 3.0901i
1.2020 + 3.0574i
1.2020 - 3.0574i
1.2766 + 3.0246i
1.2766 - 3.0246i
1.3500 + 2.9906i
1.3500 - 2.9906i
1.4225 + 2.9552i
1.4225 - 2.9552i
1.4941 + 2.9182i
1.4941 - 2.9182i
1.5648 + 2.8797i
1.5648 - 2.8797i
1.6345 + 2.8396i
1.6345 - 2.8396i
1.7033 + 2.7979i
1.7033 - 2.7979i
1.7712 + 2.7545i
1.7712 - 2.7545i
1.8379 + 2.7096i
1.8379 - 2.7096i
1.9036 + 2.6631i
1.9036 - 2.6631i
1.9682 + 2.6150i
1.9682 - 2.6150i
2.0316 + 2.5653i
2.0316 - 2.5653i
2.0938 + 2.5141i
2.0938 - 2.5141i
2.1547 + 2.4615i
2.1547 - 2.4615i
2.2143 + 2.4073i
2.2143 - 2.4073i
2.2727 + 2.3518i
2.2727 - 2.3518i
2.3297 + 2.2948i
2.3297 - 2.2948i
2.3852 + 2.2364i
2.3852 - 2.2364i
2.4394 + 2.1767i
2.4394 - 2.1767i
2.4920 + 2.1157i
2.4920 - 2.1157i
2.5432 + 2.0534i
2.5432 - 2.0534i
2.5928 + 1.9899i
2.5928 - 1.9899i
2.6409 + 1.9251i
2.6409 - 1.9251i
2.6874 + 1.8592i
2.6874 - 1.8592i
2.7322 + 1.7922i
2.7322 - 1.7922i
2.7754 + 1.7241i
2.7754 - 1.7241i
2.8170 + 1.6550i
2.8170 - 1.6550i
2.8568 + 1.5848i
2.8568 - 1.5848i
2.8949 + 1.5137i
2.8949 - 1.5137i
2.9312 + 1.4417i
2.9312 - 1.4417i
2.9657 + 1.3688i
2.9657 - 1.3688i
2.9985 + 1.2951i
2.9985 - 1.2951i
3.0294 + 1.2206i
3.0294 - 1.2206i
3.0585 + 1.1453i
3.0585 - 1.1453i
3.0858 + 1.0694i
3.0858 - 1.0694i
3.1111 + 0.9928i
3.1111 - 0.9928i
3.1346 + 0.9156i
3.1346 - 0.9156i
3.1562 + 0.8379i
3.1562 - 0.8379i
3.1758 + 0.7596i
3.1758 - 0.7596i
3.1935 + 0.6809i
3.1935 - 0.6809i
3.2093 + 0.6018i
3.2093 - 0.6018i
3.2232 + 0.5223i
3.2232 - 0.5223i
3.2350 + 0.4425i
3.2350 - 0.4425i
3.2449 + 0.3624i
3.2449 - 0.3624i
3.2648 + 0.0403i
3.2648 - 0.0403i
3.2628 + 0.1210i
3.2628 - 0.1210i
3.2529 + 0.2821i
3.2529 - 0.2821i
3.2588 + 0.2016i
3.2588 - 0.2016i

Answer 2

for i=1:100
for j=1:100
A(i,j)=1/(i-j+0.4);
end
end
lambda=eig(A)
---------------运行结果lambda为100个特征值。本回答被提问者采纳