Bounding Eigenvalues of Symmetric Positive Definite Tensors: A Comparative Analysis of TDet and TDep Approaches

This article explores bounds for the eigenvalues of symmetric positive definite (SPD) tensors. We focus on trace-determinant (TDet) and trace-dependent (TDep) bounds to understand and characterize the eigenvalues of SPD tensors. By establishing inequalities, we find both upper and lower bounds, offering insights into the tensor behavior. Additionally, we compare the effectiveness of the TDet and TDep bounds in capturing the extreme eigenvalues of SPD tensors.