Finite integrity bases for five or fewer symmetric 3×3 matrices

In a previous paper [1], finite integrity bases for five or fewer symmetric 3 × 3 matrices, under the orthogonal transformation group, have been derived. In the present paper, it will be shown that the integrity bases there derived are redundant in the sense that certain of their elements can be expressed as polynomials in the remaining elements, and integrity bases containing fewer elements will thus be obtained. The results of the previous paper [1], which form the starting point of the present paper, are essentially consequences of the Hamilton-Cayley theorem and the procedures adopted in the present paper are similarly based.