query: Do Real Symmetric Matrices have 'n' linearly independent eigenvectors?
positive_passages.docid: 18012
positive_passages.text: Eigenvectors of real symmetric matrices are orthogonal
negative_passages.docid: 17217
negative_passages.text: Linear algebra skew symmetric
negative_passages.docid: 144097
negative_passages.text: eigenvalues and eigenvectors of $vv^T$
negative_passages.docid: 35013
negative_passages.text: Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
negative_passages.docid: 27778
negative_passages.text: Eigenvalues of a real skew symmetric matrix
negative_passages.docid: 150376
negative_passages.text: Does Real Eigenvalues mean it is an hermitian Matrix
negative_passages.docid: 29454
negative_passages.text: A and B are real, symmetric and positive semi-definite matrices of the same order; is AB diagonalizable?
negative_passages.docid: 66729
negative_passages.text: For a square matrix $A$ presence of $n$ linearly independent eigenvectors implies full rank, thereby invertible?
negative_passages.docid: 14320
negative_passages.text: How to prove that eigenvectors from different eigenvalues are linearly independent
negative_passages.docid: 81176
negative_passages.text: A normal matrix with real eigenvalues is Hermitian
negative_passages.docid: 106024
negative_passages.text: The eigenvalues and corresponding eigenvectors for the matrix
negative_passages.docid: 70455
negative_passages.text: Why are all nonzero eigenvalues of the skew-symmetric real matrices pure imaginary?
negative_passages.docid: 137081
negative_passages.text: Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices?
negative_passages.docid: 24454
negative_passages.text: The relationship between the eigenvalues of matrices $XY$ and $YX$
negative_passages.docid: 120687
negative_passages.text: If the sum of eigenvectors is an eigenvector, then they all correspond to the same eigenvalue
negative_passages.docid: 3408
negative_passages.text: Do positive semidefinite matrices have to be symmetric?
negative_passages.docid: 94424
negative_passages.text: Matrices and Eigenvalues of Norm