query: Are the eigenvectors in the bases for the eigenspaces of a matrix linearly independent?
positive_passages.docid: 109675
positive_passages.text: Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
negative_passages.docid: 85581
negative_passages.text: Matrices commute if and only if they share a common basis of eigenvectors?
negative_passages.docid: 4443
negative_passages.text: Why is the determinant zero iff the column vectors are linearly dependent?
negative_passages.docid: 75536
negative_passages.text: every eigenvalue of $T$ has only one corresponding eigenvector up to a scalar multiplication
negative_passages.docid: 91636
negative_passages.text: Are all eigenvectors, of any matrix, always orthogonal?
negative_passages.docid: 53993
negative_passages.text: Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering?
negative_passages.docid: 144097
negative_passages.text: eigenvalues and eigenvectors of $vv^T$
negative_passages.docid: 151088
negative_passages.text: Finding Matrix A from Eigenvalues and Eigenvectors (Diagonalization)
negative_passages.docid: 152147
negative_passages.text: Why is a set of orthonormal vectors linearly independent?
negative_passages.docid: 61718
negative_passages.text: Can a basis for a vector space be made up of matrices instead of vectors?
negative_passages.docid: 93550
negative_passages.text: How to find the matrix representation of an operator from its action on a basis?
negative_passages.docid: 45527
negative_passages.text: Do real matrices always have real eigenvalues?
negative_passages.docid: 28584
negative_passages.text: Eigenvalues and eigenspaces of AB
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 602
negative_passages.text: How get eigenvectors without phase jump?
negative_passages.docid: 96530
negative_passages.text: Matrix representation of linear map in this basis
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$