Computing Eigenvectors from Eigenvalues In an Arbitrary Orthonormal Basis

TL;DR

This paper explores methods to compute eigenvectors from eigenvalues within arbitrary orthonormal bases, linking quadratic optimization constraints to eigenvector computation through submatrix and sub-projection eigenvalues.

Contribution

It introduces a novel approach connecting eigenvector computation to quadratic optimization constraints via submatrix and sub-projection eigenvalues.

Findings

Eigenvectors can be derived from eigenvalues of submatrices.

Eigenvalues of sub-projections relate to eigenvectors in orthonormal bases.

The method provides an alternative to traditional eigenvector computation techniques.

Abstract

The method of computing eigenvectors from eigenvalues of submatrices can be shown as equivalent to a method of computing the constraint which achieves specified stationary values of a quadratic optimization. Similarly, we show computation of eigenvectors of an orthonormal basis projection using eigenvalues of sub-projections.