eig在python中到底输出什么？

Question

我试图检索所有的（常规）特征向量以及足够的广义特征向量，以完成从我的平方NxN矩阵的基础。我的问题是，这个输出到底是什么特征向量？地址：

evals, levecs = eig(Mnp, left=True,right=False)

我所能找到的关于这个的文档只说“解决一个普通的或广义的方阵特征值问题。求一般矩阵的特征值w和左右特征向量”。你知道吗

有谁能告诉我，这是否意味着我的左特征向量是正则的和广义的？如有任何消息，我将不胜感激。你知道吗

Answer 1

从documentation

w : (…, M) array

The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be of complex type, unless the imaginary part is zero in which case it will be cast to a real type. When a is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs

v : (…, M, M) array

The normalized (unit “length”) eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i].

从那一页的笔记部分

This is implemented using the _geev LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays.

The number w is an eigenvalue of a if there exists a vector v such that dot(a,v) = w * v. Thus, the arrays a, w, and v satisfy the equations dot(a[:,:], v[:,i]) = w[i] * v[:,i] for i \in {0,...,M-1}.

The array v of eigenvectors may not be of maximum rank, that is, some of the columns may be linearly dependent, although round-off error may obscure that fact. If the eigenvalues are all different, then theoretically the eigenvectors are linearly independent. Likewise, the (complex-valued) matrix of eigenvectors v is unitary if the matrix a is normal, i.e., if dot(a, a.H) = dot(a.H, a), where a.H denotes the conjugate transpose of a.

Finally, it is emphasized that v consists of the right (as in right-hand side) eigenvectors of a. A vector y satisfying dot(y.T, a) = z * y.T for some number z is called a left eigenvector of a, and, in general, the left and right eigenvectors of a matrix are not necessarily the (perhaps conjugate) transposes of each other.