New answers tagged eigenvalue
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Why does the eigenvalues of an angular frequency matrix are the natural frequency? (INTUITION)
The acceleration is the second derivative of the position i.e. $a \equiv \ddot{x}$.
This means that the you have managed to decompose the couple system of oscillators into independent modes (to state ...
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Structural dynamics: Why are modeshape-vectors referred to as orthogonal?
No reference I encountered on the topic so far so has called the eigenmodes orthogonal with respect to the standard scalar product, for the obvious reason you point out: They are not orthogonal in ...
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Calculating eigenvalues and eigenstates of an infinite dimensional Hamiltonian
Here is an alternative, more direct method of determining eigenstates and eigenvalues (the situation is complicated by the fact that the eigenstates are not normalisable - see (3) in Tobias Fünke's ...
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Calculating eigenvalues and eigenstates of an infinite dimensional Hamiltonian
The following procedure is only on a formal level. Let $k\in [-\pi,\pi)$ and define $$|k\rangle :=\frac{1}{\sqrt{2\pi}}\sum\limits_{m\in\mathbb Z} e^{ikm}|m\rangle \tag 1 \quad .$$
Note that $|k\...
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Are the eigenvalues of the Dirac operator real?
No, the eigenvalues of the Dirac operator are in general not real. In fact, the theory of Dirac operators in Lorentzian signature is somewhat exotic - most mathematical texts consider only the ...
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