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...

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...

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...

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...

number of matrices, which are related to Spin (physics). Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices Gamma...

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...

processes. Gamma matrices — 4 × 4 matrices in quantum field theory. Gell-Mann matrices — a generalization of the Pauli matrices; these matrices are one notable...

analysis. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. The determinant of a square matrix is...

Fastest Fourier Transform in the West Generalizations of Pauli matrices Least-squares spectral analysis List of Fourier-related transforms Multidimensional...

of unitary matrices are also unitary matrices, and all quantum gates are unitary matrices. Positive integer exponents are equivalent to sequences of serially...

families of Hermitian matrices include the Pauli matrices, the Gell-Mann matrices and their generalizations. In theoretical physics such Hermitian matrices are...

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...

These matrices and the form of the wave function have a deep mathematical significance. The algebraic structure represented by the gamma matrices had been...

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...

e1, e2, e3 may be determined accordingly. Clifford algebra Generalizations of Pauli matrices DFT matrix Circulant matrix Weyl, H. (1927). "Quantenmechanik...

constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences...

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 ′ ↦ −...

Eugene Wigner) of the Dirac equation. What 9 therefore tells us, is that by applying a FW transformation to the Dirac–Pauli representation of Dirac's equation...

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...

{\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...

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 ...

Two-body Dirac equation Generalizations of Pauli matrices Wigner D-matrix Weyl–Brauer matrices Higher-dimensional gamma matrices Joos–Weinberg equation...

}{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...

the fundamental reopreserntation of S U ( 2 ) {\displaystyle SU(2)} (Pauli matrices) σ k ∗ = U σ k U † , {\displaystyle \sigma _{k}^{*}=U\sigma _{k}U^{\dagger...

{\displaystyle X_{j}} and Z j {\displaystyle Z_{j}} are 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...

real matrices were found isomorphic to coquaternions. Soon the matrix paradigm began to explain several others as they were represented by matrices and...

_{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...

as a linear combination of the Pauli matrices, which provide a basis for 2 × 2 {\displaystyle 2\times 2} self-adjoint matrices: ρ = 1 2 ( I + r x σ x +...

proposed to replace by matrices the position and momentum variables of the equations of classical mechanics. They applied the rules of matrix mechanics to...

{\displaystyle m\times m} ⁠ matrices too. In that case, "unitary" is the same as "orthogonal". Then, interpreting both unitary matrices as well as the diagonal...