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...

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...

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...

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

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

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...

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...

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

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

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...

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 ′ ↦ −...

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 ...

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...

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...

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...

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

}{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...

_{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...

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

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...

{\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...

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...