Positive Operator

A positive operator on a complex Hilbert space is a linear bounded operator for which for every vector . The inequality requires the inner product to be real and nonnegative. Such an operator is self-adjoint.

In finite dimension, this is the condition for a positive semidefinite matrix. A positive operator of trace one represents a quantum state; in finite dimension it is a density matrix.

See also

Bounded Operator, Density Matrix, Hilbert Space, Positive Semidefinite Matrix, Quantum State

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References

Anantharaman, C. and Popa, S. An Introduction to

Factors. https://www.math.ucla.edu/~popa/Books/IIun.pdf.

Cite this as:

Weisstein, Eric W. "Positive Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PositiveOperator.html

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