如何在MATLAB中找到两个矩阵的联合特征值? [英] How can I find the joint eigenvalues of two matrices in MATLAB?

问题描述

如果将矩阵 A 和 B 的联合特征值定义为方程的根 det(lambda * A - B )= 0， 如何在MATLAB中解决此问题?

If the joint eigenvalues of matrices A and B are defined as the roots of the equation det(lambda * A - B) = 0, how can I solve this in MATLAB?

尤其是，我不确定如何定义lambda －它显然需要是矩阵或向量，否则将只有一个联合特征值.另外，我不确定是否有内置函数，或者是否需要使用fzero来查找非线性函数的根.

In particular, I am not sure how exactly lambda is defined - it obviously needs to be a matrix or vector, as otherwise there would only be one joint eigenvalue. Also, I am not sure if there is any in-built function, or if, say, fzero for finding the roots of nonlinear functions needs to be used.

推荐答案

为此提供了一个内置函数.

There is a built-in function for this.

http://www.mathworks.com/help/matlab/ref/eig.html

[V,D] = eig(B,A);

[V,D] = eig(A,B)解决系统det(A - lambda*B) == 0.但是，要解决的理想系统是det(A*lambda - B) == 0，因此将输入反向以尊重对此系统的解决.

[V,D] = eig(A,B) solves the system det(A - lambda*B) == 0. However, the desired system to solve is det(A*lambda - B) == 0 and so the inputs are reversed to respect solving this system.

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