Mutual incidence matrix of two balanced incomplete block designs

2023/12/06 by Alexander Shramchenko, Vasilisa Shramchenko, Shramchenko, Alexander +1
Decision Sciences · Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2312.03937

openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose to consider a mutual incidence matrix M of two balanced incomplete block designs built on the same finite set. In the simplest case, this matrix reduces to the standard incidence matrix of one block design. We find all eigenvalues of the matrices MM^T and M^TM and their eigenspaces.

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