query: When is an orthogonal projection a unitary operator?
positive_passages.docid: 146099
positive_passages.text: Why is this true: The only orthogonal projection that is also unitary from $\Bbb C^n$ to $\Bbb C^n$ is the identity
negative_passages.docid: 90345
negative_passages.text: If $\lVert x\rVert=\lVert y \rVert$, prove that exists a unitary transformation such as $Tx=y$
negative_passages.docid: 55691
negative_passages.text: Are states of a quantum system represented by vectors in a Hilbert space?
negative_passages.docid: 63465
negative_passages.text: Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
negative_passages.docid: 93165
negative_passages.text: A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection
negative_passages.docid: 48579
negative_passages.text: How to find the orthogonal complement of a subspace?
negative_passages.docid: 26249
negative_passages.text: Self adjoint operators and trace class property
negative_passages.docid: 133609
negative_passages.text: orthonormal system in a Hilbert space
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: 16692
negative_passages.text: a representation condition of Hilbert space
negative_passages.docid: 95928
negative_passages.text: Independence and orthogonality
negative_passages.docid: 95481
negative_passages.text: The set of self-adjoint operators over a Hilbert space doesn't form a lattice
negative_passages.docid: 99942
negative_passages.text: A normal, idempotent linear operator must be self-adjoint
negative_passages.docid: 51302
negative_passages.text: Show that the operator norm is submultiplicative
negative_passages.docid: 116112
negative_passages.text: Examples of 'almost' vector spaces where unitary law fails
negative_passages.docid: 127000
negative_passages.text: When does $V = \ker(f) \oplus \operatorname{im}(f)$?
negative_passages.docid: 83220
negative_passages.text: If $U$ is unitary operator then spectrum $\sigma(U)$ is contained inside the unit circle