Pairs Of Matrices With Quadratic Minimal Polynomials
Linear Algebra And Its Applications
Let A, B be n × n matrices over a field F, and suppose A, B have quadratic minimal polynomials. Then the algebra generated by A, B has dimension at most 2n − 1 if n is odd and 2n if n is even. These bounds are exact.
F. J. Gaines, T. J. Laffey, and Helene Shapiro.
"Pairs Of Matrices With Quadratic Minimal Polynomials".
Linear Algebra And Its Applications.