Every matrix is a linear combination of three idempotents Original Research Article

It is shown that every n×n matrix over a field of characteristic zero is a linear combination of three idempotent matrices. It is proved that both 2×2 matrices and complex 3×3 matrices are linear combinations of two idempotents. Also we present 3×3 and 4×4 matrices that are not linear combinations of any two idempotents.