A Generalization of the Cayley-Hamilton Theorem

作者：Chen Lizhou^*

来源：American Mathematical Monthly, 2012, 119(4): 340-342.

DOI：10.4169/amer.math.monthly.119.04.340

Let A = [a(ij)](nxn) and B = [b(ij)](nxn) be two commuting square matrices of order n over an arbitrary commutative ring. We prove that the determinant of the matrix [b(ij)A - a(ij)B](nxn) which is regarded as an n x n block matrix with pairwise commuting entries, is exactly equal to the n x n zero matrix. If B is the identity matrix, then the result is equivalent to the Cayley-Hamilton theorem.

• 出版日期2012-4
• 单位复旦大学