Products of diagonalizable matrices (Q1381274)

A square matrix over a field \(K\) is diagonalizable if it is similar to a diagonal matrix over \(K\). Let \(\text{char} (K)\neq 2\), 3. Then every square matrix over \(K\) is a product of two diagonalizable matrices. If \(\text{char} (K)=3\) then every square matrix is a product of three diagonalizable matrices and the number 3 in general is minimal. If \(\text{char} (K)=2\) and \(\text{card} (K)\) is not less than \(d(A)+2\), then \(A\) is a product of two diagonalizable matrices. Here \(d(A)\) is the maximal degree of the elementary divisors of \(A\). In particular, if \(K\) is infinite, then every square matrix is a product of two diagonalizable matrices.