Inverse Eigenvalue Problem for Real Symmetric Seven-Diagonal Matrix

This paper presents the following inverse eigenvalue problem for real symmetric five-diagonal matrix: Question 1 Given real numbers lambda(1), lambda(2), lambda(3) (lambda(1) > lambda(2) > lambda(3)), nonzero vectors x, y, z is an element of R(n). Find n x n real symmetric seven-diagonal matrix A such that Ax = lambda(1)x, Ay = lambda(2)y, Az = lambda(3)z. Question 2 Given real numbers lambda(1), lambda(2), lambda(3) (lambda(1) > lambda(2) > lambda(3)), nonero vectors x, y, z is an element of R(n) and real numbers d(1), d(2), ..., d(n-3). Find n x n real symmetric seven-diagonal matrix T such that Tx = lambda(1)x, Ty = lambda(2)y, Tz = lambda(3)z, and d(1), d(2), ..., d(n-3) is the third minor diahonal. The expression of the solution of the problem is given, and a numerical example is provided.