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2. Spinors in three dimensions - Wikipedia

   en.wikipedia.org/wiki/Spinors_in_three_dimensions

   Given a unit vector in 3 dimensions, for example (a, b, c), one takes a dot product with the Pauli spin matrices to obtain a spin matrix for spin in the direction of the unit vector. The eigenvectors of that spin matrix are the spinors for spin-1/2 oriented in the direction given by the vector. Example: u = (0.8, -0.6, 0) is a unit vector ...

3. Spin matrix - Wikipedia

   en.wikipedia.org/wiki/Spin_matrix

   The term spin matrix refers to a number of matrices, which are related to Spin (physics). Quantum mechanics and pure mathematics.

4. Eigenspinor - Wikipedia

   en.wikipedia.org/wiki/Eigenspinor

   Suppose there is a spin 1/2 particle in a state = [].To determine the probability of finding the particle in a spin up state, we simply multiply the state of the particle by the adjoint of the eigenspinor matrix representing spin up, and square the result.

5. Pauli matrices - Wikipedia

   en.wikipedia.org/wiki/Pauli_matrices

   The analog formula to the above generalization of Euler's formula for Pauli matrices, the group element in terms of spin matrices, is tractable, but less simple. [7] Also useful in the quantum mechanics of multiparticle systems, the general Pauli group G n is defined to consist of all n-fold tensor products of Pauli matrices.

6. Spin (physics) - Wikipedia

   en.wikipedia.org/wiki/Spin_(physics)

   For example, taking the Kronecker product of two spin-⁠ 1 / 2 ⁠ yields a four-dimensional representation, which is separable into a 3-dimensional spin-1 (triplet states) and a 1-dimensional spin-0 representation (singlet state). The resulting irreducible representations yield the following spin matrices and eigenvalues in the z-basis:

7. Gell-Mann matrices - Wikipedia

   en.wikipedia.org/wiki/Gell-Mann_matrices

   These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation, so they can generate unitary matrix group elements of SU(3) through exponentiation. [1] These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann's quark ...