Certain matrices with equitable partitions have all distinct eigenvalues fully encoded in the spectrum of their equitable quotient matrix under eigenspace conditions.
Stevanović, Large sets of long distance equienergetic graphs,Ars Math
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On Matrices Whose Distinct Eigenvalues Are Fully Captured by Quotient Matrices
Certain matrices with equitable partitions have all distinct eigenvalues fully encoded in the spectrum of their equitable quotient matrix under eigenspace conditions.