The paper by Lek-Heng Lim from Stanford University introduces a variational approach to define eigenvalues, eigenvectors, singular values, and singular vectors for tensors of order \( k \geq 3 \). This approach is similar to the Rayleigh quotient method used for symmetric matrices. The key idea is to use a Lagrangian function that includes a penalty term to ensure scale invariance, typically using the \( l^k \)-norm instead of the \( l^2 \)-norm. The paper discusses the definitions and properties of these concepts for both symmetric and non-symmetric tensors, including the multilinear generalization of the Perron-Frobenius theorem. The results are illustrated with examples and applications, such as the best rank-1 approximation of tensors and the positive definiteness of homogeneous polynomial forms. The paper also explores the use of \( l^p \)-norms for different values of \( p \) and provides propositions and theorems to support the definitions and properties of these generalized concepts.The paper by Lek-Heng Lim from Stanford University introduces a variational approach to define eigenvalues, eigenvectors, singular values, and singular vectors for tensors of order \( k \geq 3 \). This approach is similar to the Rayleigh quotient method used for symmetric matrices. The key idea is to use a Lagrangian function that includes a penalty term to ensure scale invariance, typically using the \( l^k \)-norm instead of the \( l^2 \)-norm. The paper discusses the definitions and properties of these concepts for both symmetric and non-symmetric tensors, including the multilinear generalization of the Perron-Frobenius theorem. The results are illustrated with examples and applications, such as the best rank-1 approximation of tensors and the positive definiteness of homogeneous polynomial forms. The paper also explores the use of \( l^p \)-norms for different values of \( p \) and provides propositions and theorems to support the definitions and properties of these generalized concepts.