query: What is the necessary and sufficient condition for the matrix $A = I − 2xx^T $to be orthogonal?
positive_passages.docid: 6960
positive_passages.text: Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
negative_passages.docid: 80623
negative_passages.text: Must $S$ be a unitary matrix?
negative_passages.docid: 99221
negative_passages.text: Orthogonality lemma sine and cosine
negative_passages.docid: 37985
negative_passages.text: Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
negative_passages.docid: 18012
negative_passages.text: Eigenvectors of real symmetric matrices are orthogonal
negative_passages.docid: 155123
negative_passages.text: Selfadjoint Operator: Basic Criterion
negative_passages.docid: 32606
negative_passages.text: Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary
negative_passages.docid: 5616
negative_passages.text: How can I prove the IFF condition for this group of matrices?
negative_passages.docid: 101926
negative_passages.text: If $Q$ is a proper orthogonal transformation matrix, deduce that $\det(1-Q)=0$.
negative_passages.docid: 91636
negative_passages.text: Are all eigenvectors, of any matrix, always orthogonal?
negative_passages.docid: 60723
negative_passages.text: Prove that if $A$ is normal, then eigenvectors corresponding to distinct eigenvalues are necessarily orthogonal (alternative proof)
negative_passages.docid: 29230
negative_passages.text: Orthogonality of Hermite functions
negative_passages.docid: 137209
negative_passages.text: Finding the Matrix of a Linear Operator Satisfying a Polynomial
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: 140252
negative_passages.text: Matrices - Conditions for $AB+BA=0$
negative_passages.docid: 97994
negative_passages.text: Orthogonality Relations Exercise, Brezis' Book Functional Analysis
negative_passages.docid: 61274
negative_passages.text: If $AA^T$ is the zero matrix, then $A$ is the zero matrix