Invariants of tensors

In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor A {displaystyle mathbf {A} } are the coefficients of the characteristic polynomial In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor A {displaystyle mathbf {A} } are the coefficients of the characteristic polynomial where I {displaystyle mathbf {I} } is the identity operator and λ i ∈ C {displaystyle lambda _{i}in mathbb {C} } represent the polynomial's eigenvalues. The principal invariants do not change with rotations of the coordinate system (they are objective, or in more modern terminology, satisfy the principle of material frame-indifference) and any function of the principal invariants is also objective. In a majority of engineering applications, the principal invariants of (rank two) tensors of dimension three are sought, such as those for the right Cauchy-Green deformation tensor.