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1 99/1 數學系 譚必信 教授 期刊論文 發佈 Theorems on partitioned matrices revisited and their applications to graph spectra , [99-1] :Theorems on partitioned matrices revisited and their applications to graph spectra期刊論文Theorems on partitioned matrices revisited and their applications to graph spectraChang, Ting-Chung; Tam, Bit-Shun; Wu, Shu-Hui淡江大學數學學系Graph spectra; Neighborhood equivalence class; Block-stochastic matrix; Laplacian; Signless laplacianPhiladelphia: Elsevier Inc.Linear Algebra and Its Applications 434(2), pp.559-581Some old results about spectra of partitioned matrices due to Goddard and Schneider or Haynsworth are re-proved. A new result is given for the spectrum of a block-stochastic matrix with the property that each off-diagonal block has equal entries and each diagonal block has equal diagonal entries and equal off-diagonal entries. The result is applied to the study of the spectra of the usual graph matrices by partitioning the vertex set of the graph according to the neighborhood equivalence relation. The concept of a reduced graph matrix is introduced. The question of when n-2 is the second la
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