These quantities are distributed evenly within a semicircle for random symmetric systems according to the Wigner (15[1])surmise. (15[3])For non-negative systems, the existence of a unique one of (15[1])these quantities with the largest magnitude (15[1])is guaranteed by the Perron-Frobenius (15[1]-5[1])theorem. (15[1]-5[1])The (15[1])asymptotic (15[1])behavior of these quantities for the Laplace-Beltrami operator is described by Weyl’s law. If a (*) matrix is diagonalizable, (10[1])there is a basis where its entries (10[1])are all zeros (-5[1])except on the diagonal, which takes (10[1])these quantities. (10[4]-5[1])The set (10[1])of all of these (10[1]-5[1])quantities (10[2])is the spectrum. These (10[1])quantities are all real for a self-adjoin matrix, and it is usually denoted by a lowercase lambda. (10[4])The solutions of the characteristic polynomial, (10[1])for 10 points, identify these values that are the scale of its corresponding eigenvectors. ■END■ (10[1])