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...

for any signature of the metric. For example, the 2×2 Pauli matrices are a set of "gamma" matrices in three dimensional space with metric of Euclidean signature...

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...

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...

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...

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...

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...

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

}}\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...

{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...

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...

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

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...

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)...

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

spin group. Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical description of...

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...

{\displaystyle \sigma _{i}} are the Pauli matrices and α {\displaystyle \alpha } is the vector made of gamma matrices α = γ t ( γ x , γ y , γ z ) {\displaystyle...

for instance, the Pauli spin matrices are a set of gamma matrices, and the two-component complex column vectors on which these matrices act are spinors...

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

matrix representation of S3. One convenient choice is given by the Pauli matrices: x 1 + x 2 i + x 3 j + x 4 k ↦ ( x 1 + i x 2 x 3 + i x 4 − x 3 + i x...

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

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...

a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set of all n × n matrices with entries...

{\displaystyle Z_{j}} are representations of elements of the spin algebra (Pauli matrices, in the case of spin 1/2) acting on the spin variables of the corresponding...