query: Given that B is a symmetric matrix how can I show that if B can be diagonalized then there exists an orthonormal basis of eigenvectors of B?
positive_passages.docid: 18012
positive_passages.text: Eigenvectors of real symmetric matrices are orthogonal
negative_passages.docid: 125569
negative_passages.text: Prove that the eigenvalues of a real symmetric matrix are real
negative_passages.docid: 143793
negative_passages.text: If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
negative_passages.docid: 100656
negative_passages.text: $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors
negative_passages.docid: 59055
negative_passages.text: Diagonalizable transformation restricted to an invariant subspace is diagonalizable
negative_passages.docid: 103537
negative_passages.text: How to diagonalize this matrix...
negative_passages.docid: 82410
negative_passages.text: Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
negative_passages.docid: 14320
negative_passages.text: How to prove that eigenvectors from different eigenvalues are linearly independent
negative_passages.docid: 135316
negative_passages.text: A basic question on diagonalizability of a matrix
negative_passages.docid: 135420
negative_passages.text: Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.
negative_passages.docid: 110271
negative_passages.text: Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
negative_passages.docid: 79739
negative_passages.text: Block diagonal matrix diagonalizable
negative_passages.docid: 39430
negative_passages.text: Orthogonal matrix and orthonormal columns
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: 52260
negative_passages.text: Diagonalization and eigenvalues
negative_passages.docid: 97733
negative_passages.text: Can it be determined that the sum of the diagonal entries, of matrix A, equals the sum of eigenvalues of A
negative_passages.docid: 85581
negative_passages.text: Matrices commute if and only if they share a common basis of eigenvectors?