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  2. Pauli matrices - Wikipedia

    en.wikipedia.org/wiki/Pauli_matrices

    The fact that the Pauli matrices, along with the identity matrix I, form an orthogonal basis for the Hilbert space of all 2 × 2 complex matrices , over , means that we can express any 2 × 2 complex matrix M as = + where c is a complex number, and a is a 3-component, complex vector.

  3. Generalizations of Pauli matrices - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of_Pauli...

    This method of generalizing the Pauli matrices refers to a generalization from a single 2-level system to multiple such systems.In particular, the generalized Pauli matrices for a group of qubits is just the set of matrices generated by all possible products of Pauli matrices on any of the qubits.

  4. Spin matrix - Wikipedia

    en.wikipedia.org/wiki/Spin_matrix

    Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices; Gamma matrices, which can be represented in terms of the Pauli matrices.

  5. Eigenspinor - Wikipedia

    en.wikipedia.org/wiki/Eigenspinor

    In quantum mechanics, eigenspinors are thought of as basis vectors representing the general spin state of a particle. Strictly speaking, they are not vectors at all, but in fact spinors . For a single spin 1/2 particle, they can be defined as the eigenvectors of the Pauli matrices .

  6. Structure constants - Wikipedia

    en.wikipedia.org/wiki/Structure_constants

    In mathematics, the structure constants or structure coefficients of an algebra over a field are the coefficients of the basis expansion (into linear combination of basis vectors) of the products of basis vectors. Because the product operation in the algebra is bilinear, by linearity knowing the product of basis vectors allows to compute the ...

  7. Spinors in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Spinors_in_three_dimensions

    There were some precursors to Cartan's work with 2×2 complex matrices: Wolfgang Pauli had used these matrices so intensively that elements of a certain basis of a four-dimensional subspace are called Pauli matrices σ i, so that the Hermitian matrix is written as a Pauli vector. [2] In the mid 19th century the algebraic operations of this algebra of four complex dimensions were studied as ...

  8. Helicity basis - Wikipedia

    en.wikipedia.org/wiki/Helicity_basis

    The two-component helicity eigenstates satisfy ^ (^) = (^) where are the Pauli matrices, ^ is the direction of the fermion momentum, = depending on whether spin is pointing in the same direction as ^ or opposite.

  9. Algebra of physical space - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_physical_space

    The Clifford algebra Cl 3,0 (R) has a faithful representation, generated by Pauli matrices, on the spin representation C 2; further, Cl 3,0 (R) is isomorphic to the even subalgebra Cl [0] 3,1 (R) of the Clifford algebra Cl 3,1 (R). APS can be used to construct a compact, unified and geometrical formalism for both classical and quantum mechanics.