MATLAB中的eig函数

在MATLAB中，计算矩阵A的特征值和特征向量的函数是eig(A)，常用的调用格式有5种：

E=eig(A)：求矩阵A的全部特征值，构成向量E。 [V,D]=eig(A)：求矩阵A的全部特征值，构成对角阵D，并求A的特征向量构成V的列向量。 [V,D]=eig(A,'nobalance')：与第2种格式类似，但第2种格式中先对A作相似变换后求矩阵A的特征值和特征向量，而格式3直接求矩阵A的特征值和特征向量。 E=eig(A,B)：由eig(A,B)返回N×N阶方阵A和B的N个广义特征值，构成向量E。 [V,D]=eig(A,B)：由eig(A,B)返回方阵A和B的N个广义特征值，构成N×N阶对角阵D，其对角线上的N个元素即为相应的广义特征值，同时将返回相应的特征向量构成N×N阶满秩矩阵，且满足AV=BVD。

eig

Find eigenvalues and eigenvectors Syntax

d = eig(A) d = eig(A,B) [V,D] = eig(A) [V,D] = eig(A,'nobalance') [V,D] = eig(A,B) [V,D] = eig(A,B,flag)

d = eig(A)和 [V,D] = eig(A)　最为常用，注意，第一列为对应第一个特征值的特征向量。

附录：

matlab中关于eig的说明：

 EIG   Eigenvalues and eigenvectors.

E = EIG(X) is a vector containing the eigenvalues of a square　matrix X.[V,D] = EIG(X) produces a diagonal matrix D of eigenvalues and a　full matrix V whose columns are the corresponding eigenvectors so　that X*V = V*D.[V,D] = EIG(X,'nobalance') performs the computation with balancing　disabled, which sometimes gives more accurate results for certain　problems with unusual scaling. If X is symmetric, EIG(X,'nobalance')　is ignored since X is already balanced.E = EIG(A,B) is a vector containing the generalized eigenvalues　of square matrices A and B.[V,D] = EIG(A,B) produces a diagonal matrix D of generalized　eigenvalues and a full matrix V whose columns are the　corresponding eigenvectors so that A*V = B*V*D.EIG(A,B,'chol') is the same as EIG(A,B) for symmetric A and symmetric　positive definite B.  It computes the generalized eigenvalues of A and B　using the Cholesky factorization of B.EIG(A,B,'qz') ignores the symmetry of A and B and uses the QZ　algorithm. In general, the two algorithms return the same result, however using the　QZ algorithm may be more stable for certain problems.　The flag is ignored when A and B are not symmetric.