MATLAB中的eig函数

1. E=eig(A)：求矩阵A的全部特征值，构成向量E。
2. [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。
3. [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。
4. 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。
5. [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.