An Inverse Eigenvalue Problems for Two Kinds of Symmetric Matrices

In this thesis, we present the inverse eigenvalue problem for constructing two kinds of symmetric matrices which are a combination of a tridiagonal matrix and an arrowhead matrix from particular spectral information. The first spectral information is the eigenvalues of the leading principal submatrix, and the second spectral information is one of the eigenpairs and maximal eigenvalues of the leading principal submatrix. Moreover, our results generate an algorithmic procedure to compute the elements of the matrix.