Algebraic properties. All three of the Pauli matrices can be compacted into a single expression: = (− + −) where i = √ −1 is the imaginary unit, and δ ab is the Kronecker delta, which equals +1 if a = b and 0 otherwise. This expression is useful for "selecting" any one of the matrices numerically by substituting values of a = 1, 2, 3, in turn useful when any of the matrices (but no

How to prove that every matrix with trace zero can be There are several proofs of this nice result, differing in style and applicability. Some of them work for all ground fields, some for fields of characteristic [math]0[/math], and some only for [math]\R[/math] or [math]\C[/math]. I personally prefe Symplectic Matrix - an overview | ScienceDirect Topics Thus, the path naïvely traced in (2.3.2) can formally be interpreted as developing from the Lie algebra of the quadratic homogeneous polynomials in both q and p coordinates, and then proceeding through the Lie algebra of the corresponding traceless matrices, formed by Poisson bracket operation with q and p, up to the symplectic Lie group of Spin 1/2 and other 2 State Systems

## The relation between OPE and this matrix element is through operator-state correspondence. \$\endgroup\$ – Peter Kravchuk Mar 26 '17 at 22:04 \$\begingroup\$ @Peter Could you expand on this? Thinking about the problem again my take on this is as follows: \$\endgroup\$ – Kvothe Mar 27 '17 at 8:55

The bundle of simultaneously diagonalizable n-tuples of agonalization of n-tuples of matrices for its applica-tions in sciences in particular for the case of traceless matrices, [7], [8]. For example they appear founding when we must give the instanton solution of Yang-Mills ﬁeld presented in an octonion form, and it can be represented by triples of traceless matrices, [1], [6], [13].

### We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under application of the Floquet operator of a quantum map that possesses (or lacks) time reversal symmetry. We find that the rate of information gain, and hence the fidelity of

The bundle of simultaneously diagonalizable n-tuples of agonalization of n-tuples of matrices for its applica-tions in sciences in particular for the case of traceless matrices, [7], [8]. For example they appear founding when we must give the instanton solution of Yang-Mills ﬁeld presented in an octonion form, and it can be represented by triples of traceless matrices, [1], [6], [13].