Isotropic Integrity Bases for Vectors and Second-Order Tensors
In previous papers [2, 3] it has been shown how an arbitrary matrix polynomial in any number of symmetric 3 × 3 matrices may be expressed in a canonical form. From these results an integrity basis under the orthogonal transformation group for an arbitrary number of symmetric 3 × 3 matrices has been derived. This consists of traces of products formed from the matrices which have total degree six or less in the matrices. In deriving these results a number of theorems were obtained which enabled us to express a product formed from any number of 3 × 3 matrices, whether symmetric or non-symmetric, as a sum of products of particular types formed from these matrices, with coefficients which are polynomials in traces of products formed from the matrices.
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