Sentence examples for unique unitary from inspiring English sources

Consider For there exists a unique unitary polynomial of least degree such that is compact.

By means of a beautiful theorem due to E. Nelson, we prove that ωk exponentiates to a unique unitary representation of the universal covering group of SL 2,R).

Moreover, given (K, J) with the stated properties, the system (H K), W, S) is unique up to unitary equivalence, and subject to the three conditions in the conclusion.

Considering that R is a symmetric matrix, thus U=V, we can obtain a frame F determined by R according to (F=sqrt {S}V), where (sqrt {S}) is a diagonal matrix with entries the square roots of the singular values of R. The above steps bring up Algorithm 3. Recall that the frame obtained this way is unique up to unitary equivalence.

We prove that II1 factors M have a unique (up to unitary conjugacy) cross-product type decomposition around "core subfactors" N⊂M satisfying the property HT of [S. Popa, On a class of type II1 factors with Betti numbers invariants, Ann. of Math. (2) 163 (2006) 809–899] and a certain "torsion freeness" condition.

The Beurling-Lax-Halmos theorem guarantees that (Theta_{d}) and (Theta_{m}) exist and are unique up to a unitary constant right factor, and (Theta_{d}^{prime}) and (Theta_{m}^{prime}) are unique up to a unitary constant left factor.

(Note that the codebook transformation is not unique. Any right unitary rotation on matrix, with, can generate another codebook transformation (or codebook) with the same performance).

The fallacy springs from assuming that Islam (or any other religion) is a unitary and unique causal force.

The W,L pair in (12) that punctures H into a given lower triangular structure is not unique since W is non-unitary.

It is not, the reviewing attorney says, "a unitary mark with a unique, incongruous, or otherwise nondescriptive meaning in relation to the goods and/or services".

Among other interesting results, we prove that every second countable amenable group with an injective finite-dimensional representation (not necessarily unitary) is a retract of a C∗-unique group.