For a particle that has equal amplitude to move left and right, the Hermitian matrix H is zero except for nearest neighbors, where it has the value c.
22.
An old result due to Schur and Horn states that the set of possible diagonal vectors of an Hermitian matrix with given eigenvalues is the convex hull of all the permutations of the eigenvalues.
23.
To be more precise, the dynamical variable / observable is a ( not necessarily bounded ) Hermitian operator in a Hilbert space and thus is represented by a Hermitian matrix if the space is finite-dimensional.
24.
In particular, if a circulant Hermitian matrix is considered ( for example, a discretized one-dimensional Laplacian with periodic boundaries ), the orthogonality property immediately follows from the usual orthogonality of eigenvectors of Hermitian matrices.
25.
And in this formulation, the four-vector is represented as a Hermitian matrix ( the matrix transpose and complex conjugate of the matrix leaves it unchanged ), rather than a real-valued column or row vector.
26.
As with the gluon field, in a specific coordinate system and fixed gauge are traceless Hermitian matrix-valued functions, while are real-valued functions, the components of eight four-dimensional second order tensor fields.
27.
A Hermitian matrix ( or the special case of a real symmetric matrix ) or a unitary matrix is never defective; more generally, a normal matrix ( which includes Hermitian and unitary as special cases ) is never defective.
28.
More generally, an Hermitian matrix M is said to be "'positive definite "'if the scalar z ^ { * } Mz is real and positive for all non-zero column vectors z of n complex numbers.
29.
Subsequent work has strongly borne out the connection between the distribution of the zeros of the Riemann zeta function and the eigenvalues of a random Hermitian matrix drawn from the Gaussian unitary ensemble, and both are now believed to obey the same statistics.
30.
Media termed diattenuating ( or " dichroic " in the sense of polarization ), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix ( generally multiplied by a common phase factor ).
