He was a teaching professor at some dozen colleges and universities and was a Senior Mathematician at Stanford Research Institute from 1956 to 1968.
[5] He developed the idea of a characteristic root of a quaternion matrix (an eigenvalue) and shows that they must exist.
Brenner, in collaboration with Donald W. Bushaw and S. Evanusa, assisted in the translation and revision of Felix Gantmacher's Applications of the Theory of Matrices (1959).
[6] Brenner translated Nikolaj Nikolaevič Krasovskii's book Stability of motion: applications of Lyapunov's second method to differential systems and equations with delay (1963).
[9] One of the challenges in linear algebra is to find the eigenvalues and eigenvectors of a square matrix of complex numbers.
[10] In 1967 at University of Wisconsin—Madison, working in the Mathematics Research Center, he produced a technical report New root-location theorems for partitioned matrices.
Secondly, the ring of polynomials has a valuation ... a different type of regularity ..." Joel Lee Brenner was a member of the American Mathematical Society from 1936.
Beasley relates that he In 1981 Brenner and Roger Lyndon collaborated to polish an idea due to H. W. Kuhn for proving the fundamental theorem of algebra.
In the solution by Eric S. Rosenthal to a problem in the American Mathematical Monthly posted by Harry D. Ruderman,[16] Kuhn's work from 1974 was cited.