query: Prove that $-1$ is an eigenvalue of an orthogonal matrix $A \in M_{4 \times 4} (\Bbb R)$ with $\det(A)=-1$
positive_passages.docid: 155082
positive_passages.text: If $P$ is real orthogonal matrix with $\det P = -1$, prove that $-1$ is an eigenvalue of $P$.
negative_passages.docid: 88473
negative_passages.text: Proof that the trace of a matrix is the sum of its eigenvalues
negative_passages.docid: 75002
negative_passages.text: show that $\det(A)=0$ in this case
negative_passages.docid: 116136
negative_passages.text: Proof that the inverse of a square matrix is unique
negative_passages.docid: 115467
negative_passages.text: Eigenvalues of Householder matrix
negative_passages.docid: 124095
negative_passages.text: $A$ is a real orthogonal matrix, prove that $ (I+A)^{-1}(I-A)$ is skew-symmetric
negative_passages.docid: 125569
negative_passages.text: Prove that the eigenvalues of a real symmetric matrix are real
negative_passages.docid: 37537
negative_passages.text: Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
negative_passages.docid: 32487
negative_passages.text: Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
negative_passages.docid: 37249
negative_passages.text: Suppose $A$ is a 4x4 matrix such that $\det(A)=\frac{1}{64}$
negative_passages.docid: 18012
negative_passages.text: Eigenvectors of real symmetric matrices are orthogonal
negative_passages.docid: 14189
negative_passages.text: If $(I-A)(I+A)^{-1}$ is orthogonal then prove that A is skew symmetric.
negative_passages.docid: 126586
negative_passages.text: Change of basis matrix for $B_2\{(1,-1,0),(1,0,-1)\}$ to $B_1\{(0,1,-1),(1,1,-2)\}$
negative_passages.docid: 72046
negative_passages.text: Prove all eigenvalues of $A^*A$ are non-negative
negative_passages.docid: 153392
negative_passages.text: Let $A$ be a $n\times n$ matrix such that $a_{ij}=ij$,find the eigenvalues of the matrix $A$.
negative_passages.docid: 87425
negative_passages.text: Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
negative_passages.docid: 97487
negative_passages.text: How to prove whether a matrix has rank $1$