Minimal polynomial/Splits and reduced/Diagonalizable/Exercise

Let ${}M$ be an ${}n\times n$-matrix over a field ${}K$, and suppose that its minimal polynomial has the form

$(X-\lambda _{1})\cdots (X-\lambda _{k})$

with different ${}\lambda _{i}$. Show that ${}M$ is diagonalizable.

Create a solution