在MATLAB中，計算矩陣A的特征值和特征向量的函數是eig(A)，常用的調用格式有5種：

E=eig(A)：求矩陣A的全部特征值，構成向量E。

[V,D]=eig(A)：求矩陣A的全部特征值，構成對角陣D，并求A的特征向量構成V的列向量。

[V,D]=eig(A,'nobalance')：與第2種格式類似，但第2種格式中先對A作相似變換后求矩陣A的特征值和特征向量，而格式3直接求矩陣A的特征值和特征向量。

E=eig(A,B)：由eig(A,B)返回N×N階方陣A和B的N個廣義特征值，構成向量E。

[V,D]=eig(A,B)：由eig(A,B)返回方陣A和B的N個廣義特征值，構成N×N階對角陣D，其對角線上的N個元素即為相應的廣義特征值，同時將返回相應的特征向量構成N×N階滿秩矩陣，且滿足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)　最為常用，注意，第一列為對應第一個特征值的特征向量。

附錄：

matlab中關于eig的說明：

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.

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