Unitary Matrices 4.1 Basics This chapter considers a very important class of matrices that are quite use-ful in proving a number of structure theorems about all matrices. Called unitary matrices, they comprise a class of matrices that have the remarkable properties that as transformations they preserve length, and preserve the an-gle between
plicitly, the matrix elements of the adjoint representation generators are determined by the structure constants, (Fa) bc = −ifabc. (32) It is also convenient to deﬁne a set of (N2 − 1)× (N2 −1) traceless symmetric matrices (Da) bc = dabc, (33) where the dabc is deﬁned by eq. (17). Since dabb = 0 it follows that TrDa = 0. The properties Albert , Muckenhoupt : On matrices of trace zeros. On commutators of matrices over unital rings Kaufman, Michael and Pasley, Lillian, Involve: A Journal of Mathematics, 2014; Identities for the zeros of entire functions of finite rank and spectral theory Anghel, N., Rocky Mountain Journal of Mathematics, 2019; Characterization and Computation of Matrices of Maximal Trace Over Rotations Bernal, Javier and Lawrence, Jim, Journal of Geometry and Gamma matrix traceless proof | Physics Forums Oct 18, 2014 Rotation Matrices - Continuum Mechanics
Gamma matrices - Wikipedia
Symmetric Matrix - Determinant, Symmetric & Skew Symmetric
So I've had a read of this, and I'm still not convinced as to why gauge fields are traceless and Hermitian.I follow the article fine, it's just the section that says "don't worry about this complicated maths, the point is that the gauge field is in the Lie algebra".
Symmetric Matrix - Determinant, Symmetric & Skew Symmetric Properties of Symmetric Matrix. A symmetric matrix is used in many applications because of its properties. Some of the symmetric matrix properties are given below : A symmetric matrix should be a square matrix. The eigenvalue of the symmetric matrix should be a real number. If the matrix is invertible, then the inverse matrix is a symmetric matrix