Yes, if the linear operator is invertible and maps A onto A.facenian said:if subspace A is invariant with respect to a linear operator, is it true that A is invariant with respect to the inverse operator?
If invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.A. Neumaier said:Yes, if the linear operator is invertible (and hence maps A onto A).
Indeed. In infinite dimensions you need to assume more. I corrected my statement accordingly.Samy_A said:If invariant is defined as ##T(A) \subseteq A##, then I think this isn't necessarily true in an infinite dimensional space.
Wigner's 1939 paper, titled "On the Measurement of Quantum-Mechanical Operators", addresses the issue of how to measure physical quantities in the quantum mechanics framework. It introduces the concept of "Wigner's friend" as a way to understand the role of the observer in quantum measurements.
Wigner's 1939 paper is considered a groundbreaking contribution to the field of quantum mechanics. It highlights the fundamental role of the observer in the measurement process and raises important questions about the nature of reality and the limitations of our understanding of the quantum world.
In Wigner's friend thought experiment, two observers (Wigner and his friend) are each performing a measurement on a quantum system. The experiment shows that the measurement outcomes can be different depending on the observer's perspective, raising questions about the role of the observer in creating reality and the role of consciousness in quantum mechanics.
Wigner's 1939 paper highlights the issue of measurement in quantum mechanics and how it is affected by the uncertainty principle. It shows that the act of measurement itself can alter the state of the system, making it difficult to determine the exact values of physical quantities at the same time.
Wigner's 1939 paper has sparked ongoing debates and discussions about the interpretation of quantum mechanics and the role of the observer in creating reality. It has also influenced further research and developments in the field, such as the development of the Many-Worlds interpretation and quantum computing.