Well, if a matrix is unitary and hermitian, it can only have $\pm 1$ as eigenvalues. To be traceless, $N$ must be even. I ran a computer experiment. I wrote $A=UDU^\dagger$ and $B=VDV^\dagger$ where $D={\rm diag}(1^M,(-1)^M)$ and $U$, $V$ are random unitary matrices of dimension $N=2M$.

In particular, w e ha ve this sp ectral decomp osition of the unitary matrix ÒgeneratedÓ b y the an tihermitian matrix iA : U " ei A = (d k =1 |a k)ei a k (a k | I h ave b elab ored this familiar material in order to facilitate discussion of some closely related material whic h, b ecause only rarely called up on in ph ysical arXiv:1309.2921v1 [hep-th] 11 Sep 2013 In four dimensions, if a SFT is unitary, the condition that the theory is conformal (1.6) can be simplified (this follows from the unitarity bound on operator dimensions [19], see appendix A) to Vµ = ∂µL, i.e., Tµ µ = L . (1.8) Equation (1.8) is a necessary and sufficient condition for a unitary … Unitary Irreducible Representations of SL (3, R): Journal Dec 22, 2004 1 The Hamiltonian with spin - University of California ¯h ∆ϕ is a unitary operation which rotates by ∆ϕabout the z axis. (Proof:Rˆ z(∆ϕ) is exactly e−i Hˆ h¯ t for t =∆ϕ/ω 0.) Being unitary means Rˆ z(∆ϕ)† =Rˆ z(∆ϕ)−1 =Rˆ z(−∆ϕ). So aligning B with the z axis results in rotation of the spin about the z axis. Each state is restricted to the line of latitude it

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

linear algebra - If $e^{itA}$ is a special unitary matrix Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Implementability of two-qubit unitary operations over the

1 Vector spaces and dimensionality

The second term on the right describes the friction forces arising from the shear viscosity, where σ ij = ∂v i /∂x j + ∂v j /∂x i − 2δ ij ∇ · v/3 is symmetric and traceless. For a unitary gas, the evolution equation for the pressure takes a simple form because P = 2 E /3 (23, 24), where E is the local energy density (sum of the The decomposition of an arbitrary 2w × 2w unitary matrix Jul 21, 2020 Special unitary group - Accelerated Mobile Pages for Wikipedia Special unitary group In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. (More general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case.) The group operation is matrix multiplication.The special unitary group is a subgroup of the unitary group, consisting of all On isometry groups of self-adjoint traceless and skew Mar 15, 2018