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

term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes...

\gamma ^{2},\gamma ^{3}\right\}\ ,} also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they...

general Pauli group Gn is defined to consist of all n-fold tensor products of Pauli matrices. The analog formula of Euler's formula in terms of the Pauli matrices...

consisting of the 2 × 2 identity matrix I {\displaystyle I} and all of the Pauli matrices X = σ 1 = ( 0 1 1 0 ) , Y = σ 2 = ( 0 − i i 0 ) , Z = σ 3 = ( 1 0 0...

introduced the 2×2 Pauli matrices as a basis of spin operators, thus solving the nonrelativistic theory of spin. This work, including the Pauli equation, is...

description of spins, we replace the spin variables with their respective Pauli matrices. However, depending on the direction of the magnetic field, we can create...

The 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...

which normalize the n-qubit Pauli group, i.e., map tensor products of Pauli matrices to tensor products of Pauli matrices through conjugation. The notion...

Transparent dry-erase sphere used to teach spherical geometry Pauli matrices – Matrices important in quantum mechanics and the study of spin Quaternionic...

}}\equiv (\sigma _{1},\sigma _{2},\sigma _{3})} is the vector form of Pauli matrices. Matrices of this form have the following properties, which relate them intrinsically...

degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group may have complex determinants...

In practice one often writes the gamma matrices in terms of 2 × 2 sub-matrices taken from the Pauli matrices and the 2 × 2 identity matrix. Explicitly...

U(s)=e^{iKs}} Since the Pauli matrices ( σ x , σ y , σ z ) {\displaystyle (\sigma _{x},\sigma _{y},\sigma _{z})} are unitary Hermitian matrices and have eigenvectors...

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

discussing multi-qubit circuits. The Pauli gates ( X , Y , Z ) {\displaystyle (X,Y,Z)} are the three Pauli matrices ( σ x , σ y , σ z ) {\displaystyle (\sigma...

single spin 1/2 particle, they can be defined as the eigenvectors of the Pauli matrices. As such, they are vectors mathematically but physics convention distinguishes...

through Pauli matrices; see the 2 × 2 derivation for SU(2). For the general n × n case, one might use Ref. The Lie group of n × n rotation matrices, SO(n)...

{I} \end{bmatrix}}} These two 4×4 matrices are related to the Dirac gamma matrices. Note that 0 and I are 2×2 matrices here. The next step is to look for...

called the error basis (which is given by the Pauli matrices and the identity). To correct the error, the Pauli operator corresponding to the type of error...

Weyl–Brauer matrices are an explicit realization of a Clifford algebra as a matrix algebra of 2⌊n/2⌋ × 2⌊n/2⌋ matrices. They generalize the Pauli matrices to n...

mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic...

article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular...

{\displaystyle 2\times 3} ⁠. Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying...

spin operators can be represented as simple 2 × 2 matrices. These matrices are called the Pauli matrices. Creation and annihilation operators can be constructed...

Elementary matrix Exchange matrix Matrix of ones Pauli matrices (the identity matrix is the zeroth Pauli matrix) Householder transformation (the Householder...

linear combination of the Pauli matrices, which provide a basis for 2 × 2 {\displaystyle 2\times 2} self-adjoint matrices:: 126  ρ = 1 2 ( I + r x σ...

gamma matrices (known as Dirac matrices) and i is the imaginary unit. A second application of the Dirac operator will now reproduce the Pauli term exactly...

of Pauli matrices Gamma matrices, which can be represented in terms of the Pauli matrices. Higher-dimensional gamma matrices In pure mathematics and physics:...

spaces. Namely, for the spin-⁠1/2⁠ case, components of I are equal to Pauli matrices divided by 2, and so Iz = ⁠1/2⁠ τ3, where τ 3 = ( 1 0 0 − 1 ) . {\displaystyle...