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Abstract: This paper describes a generalized internally positive representation of a diagonalizable matrix and proves that its stability is equivalent to the fact that its eigenvalues belong to the ...

This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of ...

A concept that got all high school students studying mathematics swayed with the understanding of triangles – the Pythagorean theorem. A closer look at a study from 2009 found that the ancient ...

When taking the matrix exponential of an Hermitean matrix M (for example to compute the time evolution operator from the Hamiltonian of a closed system) it is sometimes faster to first diagonalize the ...

We construct a pure state on the C*-algebra 𝓑(ℓ₂) of all bounded linear operators on ℓ₂, which is not diagonalizable [i.e., it is not of the form limu⩽T(ek), ek⩾ for any orthonormal basis (ek)kϵℕ of ...

The paper provides a new construction of a pure state on the algebra of all bounded linear operators on the infinite-dimensional Hilbert space. Such pure states correspond to physical pure states of ...