Abstract Computing the roots of a scalar polynomial, or the eigenvalues of a matrix polynomial, expressed in the Chebyshev basis {𝑇𝑘(𝑥)} is a fundamental problem that arises in many applications.

Asymptotically, a real normalized eigenvalue $\lambda/\sqrt n$ of such a random matrix is uniformly distributed on the interval [ - 1, 1 ]. Analogous, but strikingly different, results are presented ...

The objectives of this course are: to develop competence in the basic concepts of linear algebra, including systems of linear equations, vector spaces, subspaces, linear transformations, the ...

The objectives of this course are: to develop competence in the basic concepts of linear algebra, including systems of linear equations, vector spaces, subspaces, linear transformations, the ...

Our analysis of model and real empirical networks is only achievable on introducing a simplifying Google-matrix reduction scheme, which in the process, yields a practical ecological eigenvalue ...

This article presents a from-scratch C# implementation of the first technique: compute eigenvalues and eigenvectors from the covariance matrix. If you're not familiar with PCA, most of the terminology ...

The transition point corresponded to a property of his matrix model called the “largest eigenvalue”: the greatest in a series of numbers calculated from the matrix’s rows and columns.

However, because the matrix was only PT-symmetric, instead of following the usual stricter symmetries, it isn’t guaranteed to have real eigenvalues — the property that would ensure that ...