partial isometry sentence in Hindi

Examples

1. Thus all sets of Kraus operators are related by partial isometries.
2. The concept of partial isometry can be defined in other equivalent ways.
3. A partially defined isometric operator with closed domain is called a partial isometry.
4. Fix two such partial isometries for the argument.
5. Thus a partial isometry is also sometimes defined as a closed partially defined isometric map.
6. A partial isometry " V " has a unitary extension if and only if the deficiency indices are identical.
7. "V " can be extended to a partial isometry acting on all of \ mathcal { H }.
8. In general, a partial isometry may not be extendable to a unitary operator and therefore a quasinormal operator need not be normal.
9. The operator " U " must be weakened to a partial isometry, rather than unitary, because of the following issues.
10. Passing to the non-commutative setting, this motivates " Krein's formula " which parametrizes the extensions of partial isometries.