A viable mean-field Hamiltonian for modelling itinerant ferromagnetism coexisting with a non-unitary spin-triplet state may after diagonalization be written as:
22.
I understand now : just because both proofs employ diagonalization and are almost identical in structure does not mean one can be reduced to the other.
23.
The first follows from direct diagonalization ( the space hierarchy theorem, NL ?" NPSPACE ) and the fact that PSPACE NPSPACE via Savitch's theorem.
24.
Note that this result does not contradict what is said on simultaneous diagonalization in the article Diagonalizable matrix, which refers to simultaneous diagonalization by a similarity transformation.
25.
Note that this result does not contradict what is said on simultaneous diagonalization in the article Diagonalizable matrix, which refers to simultaneous diagonalization by a similarity transformation.
26.
Our result here is more akin to a simultaneous diagonalization of two quadratic forms, and is useful for optimization of one form under conditions on the other.
27.
This procedure is impractical given its high computational cost : for each S _ l ^ k space, a diagonalization of the true Hamiltonian must be performed.
28.
An explicit computation of eigenvectors shows that the circle of unitaries implementing the diagonalization of Z 2 in fact connect the beginning and end points of each arc.
29.
Also, diagonalization was originally used to show the existence of arbitrarily hard complexity classes and played a key role in early attempts to prove P does not equal NP.
30.
Sequential compactness of " B " in this metric can be shown by a diagonalization argument similar to the one employed in the proof of the Arzel? Ascoli theorem.
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