query: Eigenvalue decomposition of $A = I - xx^T$
positive_passages.docid: 2271
positive_passages.text: Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
negative_passages.docid: 70157
negative_passages.text: Is every matrix $A$ such that $A^k=I$ diagonalizable?
negative_passages.docid: 106288
negative_passages.text: Prove that the eigenvalues of a block matrix are the combined eigenvalues of its blocks
negative_passages.docid: 144097
negative_passages.text: eigenvalues and eigenvectors of $vv^T$
negative_passages.docid: 158724
negative_passages.text: Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
negative_passages.docid: 136643
negative_passages.text: Continuity of eigenvalues and spectral radius for a general matrix
negative_passages.docid: 149923
negative_passages.text: eigenvalues of A - aI in terms of eigenvalues of A
negative_passages.docid: 109471
negative_passages.text: The eigenvectors of the transpose operator
negative_passages.docid: 50384
negative_passages.text: A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
negative_passages.docid: 55388
negative_passages.text: Finding nilpotent and diagonalizable operators for a linear transformation $T$
negative_passages.docid: 52260
negative_passages.text: Diagonalization and eigenvalues
negative_passages.docid: 106024
negative_passages.text: The eigenvalues and corresponding eigenvectors for the matrix
negative_passages.docid: 6960
negative_passages.text: Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
negative_passages.docid: 4952
negative_passages.text: Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
negative_passages.docid: 61538
negative_passages.text: Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
negative_passages.docid: 73952
negative_passages.text: Upper bound for the sum of absolute values of the eigenvalues
negative_passages.docid: 143793
negative_passages.text: If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite