query: Does $U^*U=I$ imply $UU^*=I$?
positive_passages.docid: 3301
positive_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 36602
negative_passages.text: $a^m=b^m$ and $a^n=b^n$ imply $a=b$
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 39755
negative_passages.text: In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
negative_passages.docid: 83220
negative_passages.text: If $U$ is unitary operator then spectrum $\sigma(U)$ is contained inside the unit circle
negative_passages.docid: 87265
negative_passages.text: If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
negative_passages.docid: 122166
negative_passages.text: Significance of $i$ in the Schrödinger equation
negative_passages.docid: 79486
negative_passages.text: Does every hermitian operator represent a measurable quantity?
negative_passages.docid: 152665
negative_passages.text: $A^TA+I$ is always invertible?
negative_passages.docid: 75466
negative_passages.text: During U-substitution, is the $du$ that we use as the infinitesimal in $\int f(u) \ du$ changing size?
negative_passages.docid: 144019
negative_passages.text: A strictly positive operator is invertible
negative_passages.docid: 156178
negative_passages.text: Do counit-unit adjunctions have the expected universal properties?
negative_passages.docid: 141286
negative_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 47313
negative_passages.text: What is $i^i$ and $(i^i)^i$
negative_passages.docid: 34147
negative_passages.text: $\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
negative_passages.docid: 82464
negative_passages.text: $U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces