If is diagonal, then the last equation follows from the usual properties of the exponential and the definition of the exponential of a matrix.) If is real then is excluded by this result. If is traceless (and only if, given that it is real), then
Traces definition, a surviving mark, sign, or evidence of the former existence, influence, or action of some agent or event; vestige: traces of an advanced civilization among the ruins. See more. Traceless | Definition of Traceless by Merriam-Webster Trace definition is - a minute and often barely detectable amount or indication. How to use trace in a sentence. Synonym Discussion of trace. traceless - Wiktionary That has no traces· That cannot be traced; untraceable Definition from Wiktionary, the free dictionary
Any matrix is similar to its Jordan form, which is upper triangular. From this points of view, the only information that you get from the matrix being traceless is that the sum of the eigenvalues is zero.
Pauli and Dirac matrices | Mathematics for Physics Δ It is important to remember that the Dirac matrices are matrix representations of an orthonormal basis of the underlying vector space used to generate a Clifford algebra. So the Dirac and chiral bases are different representations of the orthonormal basis which generates the matrix representation \({C\mathbb{^{C}}(4)\cong\mathbb{C}(4)}\) acting on vectors (spinors) in \({\mathbb{C}^{4}}\). traceless definition | English definition dictionary | Reverso
quantum mechanics - Why is there this relationship between
Definition of a Hermitian Matrix A square matrix A is Hermitian if A 5 A*. Similar results can be obtained for Hermitian matrices of order In other words, a square matrix A is Hermitian if and only if the following two conditions are met. 1. The entries on the main diagonal of A are real. 2. The entry in the ith row and the jth column is the Mathematical properties and physical meaning of the