Here, a few classes of such matrices are summarized. This method of generalizing the Pauli matrices refers to a generalization from a single 2-level system...
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In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...
44 KB (7,416 words) - 16:25, 12 July 2024
Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong...
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Spin matrix (redirect from Spin matrices)
number of matrices, which are related to Spin (physics). Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices Gamma...
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special unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary...
34 KB (5,711 words) - 10:42, 17 August 2024
Discrete Fourier transform (section Generalizations)
matrix Fast Fourier transform FFTPACK FFTW Generalizations of Pauli matrices Least-squares spectral analysis List of Fourier-related transforms Multidimensional...
72 KB (11,236 words) - 07:45, 27 August 2024
Qutrit (category Units of information)
capable of expressing any single-qutrit gate in U(3), as a series circuit of at most 9 gates. Gell-Mann matrices Generalizations of Pauli matrices Mutually...
11 KB (1,452 words) - 04:45, 31 July 2024
Hermitian matrix (redirect from Hermitian matrices)
families of Hermitian matrices include the Pauli matrices, the Gell-Mann matrices and their generalizations. In theoretical physics such Hermitian matrices are...
20 KB (3,013 words) - 18:34, 4 August 2024
Matrix (mathematics) (redirect from Applications of matrices)
as such. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. Square matrices of a given dimension...
106 KB (13,107 words) - 02:49, 27 August 2024
processes. Gamma matrices — 4 × 4 matrices in quantum field theory. Gell-Mann matrices — a generalization of the Pauli matrices; these matrices are one notable...
31 KB (1,336 words) - 00:12, 30 November 2023
Trace (linear algebra) (redirect from Trace of a matrix)
misnomer, but widely used, such as in the Pauli Matrices. It can be proven that the trace of a matrix is the sum of its eigenvalues (counted with multiplicities)...
36 KB (5,385 words) - 17:42, 20 July 2024
Generalized Clifford algebra (redirect from Clock and shift matrices)
e1, e2, e3 may be determined accordingly. Clifford algebra Generalizations of Pauli matrices DFT matrix Circulant matrix Weyl, H. (1927). "Quantenmechanik...
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Two-body Dirac equation Generalizations of Pauli matrices Wigner D-matrix Weyl–Brauer matrices Higher-dimensional gamma matrices Joos–Weinberg equation...
20 KB (2,501 words) - 13:49, 23 December 2023
Spin (physics) (section Pauli matrices)
mechanics of multiparticle systems, the general Pauli group Gn is defined to consist of all n-fold tensor products of Pauli matrices. The analog formula of Euler's...
72 KB (10,551 words) - 06:46, 30 July 2024
Dirac equation (section Pauli theory)
These matrices and the form of the wave function have a deep mathematical significance. The algebraic structure represented by the gamma matrices had been...
78 KB (12,973 words) - 07:01, 30 August 2024
Quantum logic gate (section Pauli gates (X,Y,Z))
the three Pauli matrices ( σ x , σ y , σ z ) {\displaystyle (\sigma _{x},\sigma _{y},\sigma _{z})} and act on a single qubit. The Pauli X, Y and Z equate...
74 KB (10,114 words) - 17:26, 16 August 2024
Cayley–Hamilton theorem (category Pages that use a deprecated format of the math tags)
stated the result for 3 × 3 and smaller matrices, but only published a proof for the 2 × 2 case. As for n × n matrices, Cayley stated “..., I have not thought...
65 KB (11,169 words) - 09:24, 16 July 2024
Exchange interaction (redirect from Pauli repulsion)
constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences...
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Density matrix (redirect from Density matrices)
combination of the Pauli matrices, which together with the identity matrix provide a basis for 2 × 2 {\displaystyle 2\times 2} self-adjoint matrices:: 126 ...
36 KB (5,245 words) - 19:07, 29 June 2024
3D rotation group (redirect from Set of 3D rotations)
For uniform normalization of the generators in the Lie algebra involved, express the Pauli matrices in terms of t-matrices, σ → 2i t, so that a ′ ↦ −...
65 KB (11,405 words) - 08:44, 10 June 2024
Foldy–Wouthuysen transformation (section Correspondence between the Dirac–Pauli and Newton–Wigner representations, for a fermion at rest)
the unit vector oriented in the direction of the fermion momentum. The above are related to the Dirac matrices by β = γ0 and αi = γ0γi, with i = 1, 2, 3...
27 KB (3,113 words) - 21:29, 15 August 2024
Positive-real function (category Types of functions)
function, the number of poles and number of zeroes differ by at most one. A couple of generalizations are sometimes made, with intention of characterizing the...
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Quaternion (redirect from Methods of quaternions)
use 2 × 2 complex matrices, and the other is to use 4 × 4 real matrices. In each case, the representation given is one of a family of linearly related...
96 KB (12,653 words) - 17:28, 27 August 2024
Matrix exponential (redirect from Exponential of a matrix)
square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups...
55 KB (10,413 words) - 20:04, 7 June 2024
}{4}}}Z} and { I , X , Y , Z } {\displaystyle \{I,X,Y,Z\}} are the Pauli matrices. The trace preserving condition is satisfied by the fact that ∑ i K...
8 KB (1,324 words) - 18:56, 26 August 2024
_{y}\partial _{y},} where σi are the Pauli matrices. Note that the anticommutation relations for the Pauli matrices make the proof of the above defining property...
9 KB (1,251 words) - 18:47, 29 April 2024
Hypercomplex number (category History of mathematics)
real matrices were found isomorphic to coquaternions. Soon the matrix paradigm began to explain several others as they were represented by matrices and...
26 KB (3,143 words) - 02:20, 13 August 2024
{\displaystyle Z_{j}} are N × N {\displaystyle N\times N} generalisations of the Pauli matrices satisfying Z j X k = e 2 π i N δ j , k X k Z j {\displaystyle Z_{j}X_{k}=e^{{\frac...
5 KB (965 words) - 18:09, 27 April 2024
Schrödinger equation (category Functions of space and time)
Dirac by taking the so-called square-root of the Klein-Gordon operator and in turn introducing Dirac matrices. In a modern context, the Klein-Gordon equation...
74 KB (10,232 words) - 09:07, 10 August 2024
Dual number (redirect from Ring of dual numbers)
matrix whose square is the zero matrix; that is, in the case of 2×2 matrices, any nonzero matrix of the form ( a b c − a ) {\displaystyle...
19 KB (2,757 words) - 01:02, 30 June 2024