The present invention provides an eigenvalue decomposition apparatus that can perform processing in parallel at high speed and high accuracy. The eigenvalue decomposition apparatus comprises a matrix dividing portion 14 that repeatedly divides a symmetric tridiagonal matrix T into two symmetric tridiagonal matrices, an eigenvalue decomposition portion 15 that performs eigenvalue decomposition on the symmetric tridiagonal matrix after the division, an eigenvalue computing portion 17 that repeatedly computes eigenvalues of the symmetric tridiagonal matrix that is the division origin and matrix elements of the symmetric tridiagonal matrix that is the division origin, based on eigenvalues and matrix elements obtained by eigenvalue decomposition performed by the eigenvalue decomposition portion 15, the matrix elements being part of elements of orthogonal matrices constituted by eigenvectors, until an eigenvalue of the symmetric tridiagonal matrix T is computed, and an eigenvector computing portion 19 that computes an eigenvector of the symmetric tridiagonal matrix T based on the symmetric tridiagonal matrix T and the eigenvalue thereof using twisted factorization.