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...

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

matrix Fast Fourier transform FFTPACK FFTW Generalizations of Pauli matrices Least-squares spectral analysis List of Fourier-related transforms Multidimensional...

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...

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...

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

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...

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

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)...

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

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

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

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...

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...

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...

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 ...

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...

square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups...

{\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...

quaternions (in the form of the famous Pauli spin matrices) furthered their interest; quaternions helped to understand how rotations of electrons by 360° can...

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...

}{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...

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...

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...

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...