eigenvalues love

# eigenvalues

## Definitions

• n. Plural form of eigenvalue.

## Etymologies

Sorry, no etymologies found.

## Examples

• My intuition on this is that a better model of the eigenvalues is the Boltzmann distribution, with the values as energy levels rather than strategies, which seems to complex for the PCA.

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• One of the underlying assumptions of general relativity is that spacetime can be represented by a Lorentzian manifold with signature (+, -, -, -) or (-, +, +, +) – where the signature of a metric tensor is just the number of positive and negative eigenvalues of the corresponding real symmetric matrix once it is diagonalised.

• It can shown that since the eigenvalues of the two subsystems are equal that S(A) = S(B) and that S = 0.

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• No one was in doubt about how to solve for eigenvalues of a matrix or otherwise implement the idea covered in the patent.

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• Hermitian operators in the Hilbert space associated with a system represent physical quantities, and their eigenvalues represent the possible results of measurements of those quantities.

Quantum Mechanics

• In the case that the vector is normalized, it will, from (3.1), represent a possible state of the system, and in the event that it is the sum of a pair of eigenvectors of an observable B with distinct eigenvalues, it will not itself be an eigenvector of B, but will be associated, from (3. 4b), with a set of probabilities for showing one or another result in B-measurements.

Quantum Mechanics

• Hermitean operators are linear operators, which have only real eigenvalues.

Quantum Mechanics

• In case of a perfect detector these two states should be orthogonal (because they should be eigenstates of some observable corresponding to different eigenvalues that tell you through which slit the electron went) and then the interference pattern will vanish.

Quantum Hyperion

• The only thing which is real are the eigenvalues of Hermitian operators.

Quantum Hyperion

• In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced — there must be at least one accumulation point.

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