I’m happy to share that my new mathematics preprint is now available on arXiv:

Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations

The question behind the paper is simple to state:

Can additional mathematical structure turn a problem that is not computable in general into one that is computable?

In numerical linear algebra, we often exploit symmetry to transform a whole class of matrices into a simpler block-diagonal form. In computable analysis, however, even basic quantities such as the rank of a real matrix can fail to be computable when the matrix is given only through arbitrarily accurate approximations.

In this paper, I show that for matrix classes arising from finite-group symmetries, the group structure provides enough discrete information to overcome this obstruction and uniformly compute the relevant isotypic block decomposition.

The paper also connects this construction with structured QR and QX factorizations, including the centrosymmetric case that I worked on previously.

Preliminary results from this work were presented at CCA 2026 in Trier.

arXiv: 2610.02547
https://arxiv.org/abs/2610.02547