query: Show that $\pm 1$ are the only eigenvalues of the linear operator $f$ as the transpose of a matrix
positive_passages.docid: 18939
positive_passages.text: Eigenvalues of the transpose
negative_passages.docid: 4517
negative_passages.text: Showing a $2\times2$ matrix is invertible
negative_passages.docid: 90576
negative_passages.text: Symmetric matrix eigenvalues
negative_passages.docid: 69980
negative_passages.text: Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
negative_passages.docid: 52208
negative_passages.text: Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
negative_passages.docid: 103839
negative_passages.text: Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
negative_passages.docid: 42799
negative_passages.text: Let $x$ and $y$ be two non-zero $n × 1$ vectors. If $y^T$ denotes the transpose of $y$, what are the eigenvalues of the $n × n$ matrix $xy^T$
negative_passages.docid: 16439
negative_passages.text: What are the eigenvalues of matrix that have all elements equal 1?
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 5058
negative_passages.text: Eigenvalues of the rank one matrix $uv^T$
negative_passages.docid: 149086
negative_passages.text: Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
negative_passages.docid: 125569
negative_passages.text: Prove that the eigenvalues of a real symmetric matrix are real
negative_passages.docid: 67990
negative_passages.text: Commutativity of matrix and its transpose
negative_passages.docid: 136643
negative_passages.text: Continuity of eigenvalues and spectral radius for a general matrix
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: 54668
negative_passages.text: Proof for the completeness of eigenfunctions of a self-adjoint operator
negative_passages.docid: 108012
negative_passages.text: A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$