calculation of the exponent of a matrix

Question

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

score 1 · Accepted Answer · answered Feb 25 '16 at 02:41

1

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.

answered Feb 25 '16 at 02:41

carmichael561

53,688

I entered exp({{-1,0},{0,-1}}). – user314849 Feb 25 '16 at 02:45
It probably treated this as a list, not a matrix. Try MatrixExp instead. – carmichael561 Feb 25 '16 at 02:46
Thank you so much! It worked. – user314849 Feb 25 '16 at 02:49

calculation of the exponent of a matrix

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