Nayak, SnigdhashreeSnigdhashreeNayakPanigrahy, KrushnachandraKrushnachandraPanigrahyMishra, DebasishaDebasishaMishraMishra, NachiketaNachiketaMishra2025-10-212025-10-212025-08-0110.21136/AM.2025.0022-252-s2.0-105018667642http://repository.iitgn.ac.in/handle/IITG2025/33314The tensor eigenvalue problem has been widely studied in recent years. In this paper, several new properties of eigenvalues and determinants of tensors are explored. We also proposed a formula to compute the determinant of a tensor as a mimic of the matrix determinant. The Perron-Frobenius theorem, one of the most important results in non-negative matrix theory, is proposed for the class of non-negative tensors in the Einstein product framework. Further, the power method, a widely used matrix iterative method for finding the largest eigenvalue, is framed for tensors using the Einstein product. The proposed higher-order power method is applied to calculate the largest eigenvalue of the Laplacian tensors associated with hyper-stars and hyper-trees. The numerical results show that the higher-order power method with the Einstein product is stable.false15A18 | 15A69 | determinant | eigentensor | eigenvalue | Einstein product | power methodArticle15729109563-594August 20250arArticleWOS:001592014000001