New M-Eigenvalue Inclusion Sets for Fourth-Order Partially Symmetric Tensors with Applications

The M-positive definiteness for fourth-order partially symmetric tensors plays important roles in the theory of nonlinear elasticity. Some sufficient conditions of the M-positive definiteness for fourth-order partially symmetric tensors are given based on two new M-eigenvalue inclusion sets for fourth-order partially symmetric tensors. These M-eigenvalue inclusion sets also provide upper bounds for the M-spectral radius of fourth-order partially symmetric tensors.