Could you, please, help me to understand what I am doing wrong: I am calculating exp(A), where A=[-1 0;0 -1] By my calculation with series, I got [1/e -1,0;0, 1/e-1]. Matlab and Wolfram give me [1/e,1;1;1/e]. Rules in Perko "differential Equations..." give me [1/e, 0;0, 1/e].
please, kindly explain why I got three different answers. Thank you. Verba
If $D$ is a diagonal matrix with entries $d_1,\dots,d_n$, then $e^D$ is a diagonal matrix with entries $e^{d_1},\dots,e^{d_n}$. This follows from the power series definition of $e^D$.
What exactly did you enter into Wolfram? When I tried it in Mathematica I got the right answer.