A complete flag on an inner product space has an essentially unique orthonormal basis : it is unique up to multiplying each vector by a unit ( scalar of unit length, like 1,-1, " i " ).
32.
This folk-revival environment helped the more educated members of the community to obtain an awareness of the value of musical tradition and authenticity, and therefore to resist the growing trend of fashionable Gypsy Music ( a music based on the commercial myth of an essentially unique Gypsy Music spanning from India to Spain ).
33.
By spectral theory, there is an essentially unique measure ? on the locally compact space " X " and a unitary transformation " U " between " H " 0 and " L " 2 ( " X ", ? ) which carries the operators in \ mathfrak { A } onto the corresponding multiplication operators.
34.
If an unbiased estimator of g ( \ theta ) exists, then one can prove there is an essentially unique MVUE . Using the Rao Blackwell theorem one can also prove that determining the MVUE is simply a matter of finding a sufficient statistic for the family p _ \ theta, \ theta \ in \ Omega and conditioning " any " unbiased estimator on it.
35.
Pioneering electronic music experimenters like Leon Theremin, Louis and Bebe Barron, Christopher R . Morgan, and Raymond Scott had built sound-generating devices and systems of varying complexity, and several large electronic synthesizers ( e . g . the RCA Mark II Sound Synthesizer ) had been built before the advent of the Moog, but these were essentially unique, custom-built devices or systems.
36.
I'm not a master of wiki policy ( or of wine ), but it seems to me that the claims they're marshalling to discount pieces of coverage are extrinsic to notability-- and very intrinsic to the wine enthusiast world . ( The gravity press system that makes them essentially unique in VA, they say, is just a revival of older Greco-Roman techniques.
37.
In the finite-length situation, decomposition into indecomposables is particularly useful, because of the Krull-Schmidt theorem : every finite-length module can be written as a direct sum of finitely many indecomposable modules, and this decomposition is essentially unique ( meaning that if you have a different decomposition into indecomposable, then the summands of the first decomposition can be paired off with the summands of the second decomposition so that the members of each pair are isomorphic ).
38.
Maximal compact subgroups of connected Lie groups are usually " not " unique, but they are unique up to conjugation, meaning that given two maximal compact subgroups " K " and " L ", there is an element " g " " " G " such that " gKg " " 1 = " L " hence a maximal compact subgroup is essentially unique, and people often speak of " the " maximal compact subgroup.
