An n x n matrix A is called nilpotent if an integer m exists with A'" O. Show that if A is an eigenvalue of a nilpotent matrix, then A = 0.
Section 1.2: Basic Ideas and Terminology Definition 1.2.1: A differential equation is an equation involving one or more derivatives of an unknown function. To begin our study of differential equation we need some common terminology. If an equation involves the derivative of one variable with respect with another, then the former is called a dependent variable and the later an independent variable. Example 1: d x dx a kx 0 dt2 dt A differential equation involving ordinary derivatives with respect to a single independent variable is called an ordinary differential equation. A differential equation