partial isometry वाक्य
उदाहरण वाक्य
मोबाइल
- Thus all sets of Kraus operators are related by partial isometries.
- The concept of partial isometry can be defined in other equivalent ways.
- A partially defined isometric operator with closed domain is called a partial isometry.
- Fix two such partial isometries for the argument.
- Thus a partial isometry is also sometimes defined as a closed partially defined isometric map.
- A partial isometry " V " has a unitary extension if and only if the deficiency indices are identical.
- "V " can be extended to a partial isometry acting on all of \ mathcal { H }.
- In general, a partial isometry may not be extendable to a unitary operator and therefore a quasinormal operator need not be normal.
- The operator " U " must be weakened to a partial isometry, rather than unitary, because of the following issues.
- Passing to the non-commutative setting, this motivates " Krein's formula " which parametrizes the extensions of partial isometries.
- More specifically, finding self-adjoint extensions, with various requirements, of symmetric operators is equivalent to finding unitary extensions of suitable partial isometries.
- The Toeplitz structure of " A " means that a " truncated " shift is a partial isometry on \ mathcal { H }.
- In that case, the solutions to the problem are in bijective correspondence with minimal unitary extensions of the partial isometry " V ".
- In that case, the operator is a partial isometry, that is, a unitary operator from the range of " T " to itself.
- A similar but weaker statement holds for the partial isometry : " U " is in the von Neumann algebra generated by " A ".
- A similar but weaker statement holds for the partial isometry : the polar part " U " is in the von Neumann algebra generated by " A ".
- T is the partial isometry that vanishes on the orthogonal complement of " U " and " A " is the isometry that embeds " U " into the underlying vector space.
- This is because that in the finite dimensional case, the partial isometry " U " in the polar decomposition " A " = " UP " can be taken to be unitary.
- When " B " 1 and " B " 2 are not assumed to be minimal, the same calculation shows that above claim holds verbatim with " U " being a partial isometry.
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