IN THIS PAPER, FOR GIVEN N eigenvalueS L1, L2, ..., LN, WE CONSTRUCT A JACOBI MATRIX JÎ RN×N. ALSO, THE ALGORITHM AND NUMERICAL EXAMPLES OF THIS METHOD WILL BE EXPRESSED.

CONSIDER AN N ´N MATRIX POLYNOMIAL P (L) AND A SET S CONSISTING OF K£N DISTINCT COMPLEX NUMBERS. A PERTURBATION OF P (L), SUCH THAT THE SPECTRUM OF THE PERTURBED MATRIX POLYNOMIAL INCLUDES THE SPECIFIED SET S, WAS RECENTLY CONSTRUCTED BY KOKABIFAR, LOGHMANI, PSARRAKOS AND KARBASSI (2015). IN THIS ARTICLE, WE BRIEFLY DISCUSS ON Inverse eigenvalue problem FOR THE CASE OF MATRIX POLYNOMIALS AS A CONCEIVABLE APPLICATION OF THE TOPIC OF THE PAPER.

IN THIS PAPER, WE CONSIDER CONSTRUCTING OF PSEUDO-SYMMETRIC JACOBI MATRICES. WE DENOTE THE MATRIX OBTAINED BY KNOKING THE (M+1) TH ROW AND COLUMN OF THE MATRIX J BY JM+1. USING TWO SPECTRA, THE SPECTRUM OF PSEUDO- SYMMETRIC JACOBI MATRIX J AND SPECTRUM OF MATRIX JM+1, WE PROPOSE AN ALGORITHM FOR CONSTRUCTING THE ORIGINAL MATRIX J. WE GIVE CONDITIONS ON GIVEN SPECTRAL DATA FOR EXISTENCE AND UNIQUELY RECONSTRUCTION.

IN THIS PAPER FOR A GIVEN SET OF REAL NUMBERS L1, L2,..., LN  THAT SATISFIES IN CONDITIONS (FORMULA) WE CONSTRUCT A DISTANCE MATRIX WITHOUT THE USE OF ANY HADAMARD MATRIX.

THIS ARTICLE CONSIDER AN Inverse eigenvalue problem FOR NONNEGATIVE BISYMMETRIC MATRICES OF ORDER TWO TO FOUR. WE FIRST DISCUSS THE SPECIFIED STRUCTURE OF BISYMMETRIC MATRICES, THEN FOR A GIVEN SET OF REAL NUMBERS WITH SPECIAL CONDITION, WE CONSTRUCT A NONNEGATIVE BISYMMETRIC MATRIX SUCH THAT THE GIVEN SET IS ITS SPECTRUM.

IN THIS PAPER WE SOLVE THE Inverse eigenvalue problem OF NONNEGATIVE BISYMETRIC MATRICES. WE TRY TO PRESENT SOME NECESSARY AND SUFFICENT CONDITIONS TO SOLVE THIS problem FOR ORDER 3 AND 4.