One method for calculating these does repeated factorizations into orthogonal and upper triangular components.
The second of these quantities for a d-regular graph G is greater than or equal to d minus two times the edge expansion of G . For regular non-negative systems, there exists a unique maximal one by the Perron-Frobenius theorem, which implies that for a regular Markov chain, the largest of these is one. One method for calculating these does repeated factorizations into orthogonal and upper triangular components. These can be found through the QR algorithm and by finding the roots of the characteristic polynomial. The sum of these are equal to the trace and their product is equal to the determinant. For 10 points, name these non-zero numbers for a given square matrix that when multiplied with the eigevector equals the matrix times the eigenvector.
The second of these quantities for a d-regular graph G is greater than or equal to d minus two times the edge expansion of G .
eigenvalues