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math.RA2023
The formula ABA=Tr(AB)A for matrices
Grigore Calugareanu
We prove that this formula characterizes the square matrices over commutative rings for which all 2 x 2 minors equal zero.
math.AC2023
On matrix invertible extensions over commutative rings
Grigore Calugareanu, Horia F. Pop, Adrian Vasiu
We introduce the class E2 (resp. SE2) of commutative rings R with the property that each unimodular 2 x 2 matrix with entries in R extends to an invertible 3 x 3 matrix (resp. inve…