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2.8 Exponential of a Pauli vector. ... In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, ...
the matrix exponential reduces to a plain product of the exponentials of the two respective pieces. This is a formula often used in physics, as it amounts to the analog of Euler's formula for Pauli spin matrices, that is rotations of the doublet representation of the group SU(2).
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. [1]
The Pauli matrices also anti-commute, for example = =. The matrix exponential of a Pauli matrix is a rotation operator, often ...
Pauli matrices: A set of three 2 × 2 complex Hermitian and unitary matrices. ... Matrix exponential — defined by the exponential series.
The Pauli matrices abide by the physicists' convention for Lie algebras. In that convention, Lie algebra elements are multiplied by i , the exponential map (below) is defined with an extra factor of i in the exponent and the structure constants remain the same, but the definition of them acquires a factor of i .
The exponential functions arise by definition as those limits, ... the Pauli matrices are the generators of the special unitary group in two dimensions, denoted SU(2 ...
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 ...