Invariant symmetric block matrices for the design of mixture experiments Original Research Article

The paper analyzes a quadratic subspace of block matrices which are invariant under the action of a group image arising from the design of mixture experiments. There are two sets of novel results: first, we find an orthogonal basis of the quadratic subspace and a multiplication table for the matrix blocks allowing efficient handling of image-invariant symmetric matrices. Second, we present a spectral analysis of image-invariant symmetric matrices. The results are used to calculate optimal designs of mixture experiments analytically as well as numerically.