Toloza: Exponentially accurate semiclassical asymptotics of low- lying eigenvalues for 2 x 2 matrix Schr¨odinger operators. J. Math. Anal. Appl. 312 (2005), no. 1, 300-329.G. A. Hagedorn and J. H. Toloza: Exponentially Accurate Semiclassical Asymptotics of Low- Lying Eigenvalues for 2 ...
entries, and that is related to some of the matrix algebraic properties. For example, and most importantly, a matrix is invertible if and only if its determinant is non-zero. We can only compute determinants of square matrices of the form NxN - this means, matrices 2x2, 3x3, 4x4, etc...
Array formulas are frequently used for data analysis, conditional sums and lookups, linear algebra, matrix math and manipulation, and much more. A new Excel user might come across array formulas in other people's spreadsheets, but creating array formulas is typically an intermediate-to-advanced top...
Powers of a matrix and a formula for the moduli of its eigenvaluesThe spectral radius of a complex square matrix A is given by ρ(A) = lim supk →∞ (TrAk)1/k. A more general result is proved which gives information about the moduli of all eigenvalues of A.doi:10.1016/0024-3795(...
We also prove that the characteristic and the minimal polynomials of a constructed tridiagonal matrix are equal to each other. As an application of the qd formula, we present a procedure for getting a tridiagonal matrix with specified multiple eigenvalues. Examples are given through providing with ...
MATRIX multiplicationsINVERSE problemsEIGENVALUESVECTOR spacesSYMMETRIC functionsEIGENFUNCTIONSThe Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in...