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.
KeywordsMatrix Product Symmetric Matrice Orthogonal Group Matrix Polynomial Outer Product
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