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I would like to use wolfram alpha to compute matrix exponential. I have tried with the exponential of the identity matrix, with this input:

exp({{1,0},{0,1}})

But what I get is unexpected. The input is interpreted correctly, but the result is

{{e,1},{1,e}}

while, being a diagonal matrix, I would expect {{e,0},{0,e}}... as is explained by wolfram itself.

What I'm missing?

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It's applying the exponential function element-wise, rather than computing the matrix exponential.

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    $\begingroup$ Now I got it... MatrixExp is the right function to use. $\endgroup$ – Emanuele Paolini Nov 27 '14 at 22:13
  • $\begingroup$ Yup, that's also true of numerical languages like numpy. They assume elementwise, rather than special things like matrix exponentials. Just something to consider. :) $\endgroup$ – FundThmCalculus Nov 29 '14 at 4:36
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It only proves that you cannot rely on calculators and computer algebra systems and internet queries to solve problems for you... and that none of it is a substitute for the human brain.

Im glad you found the right function to use... but had you not thought about it and blindly went along, like most people do, youd be wrong and everything that stems from it would be wrong too. But you shouldnt ever assume that the function you need is built in, or that it is coded correctly, or that you are even using the right function, and you certainly shouldnt take it on blind faith.

In my humble opinion, a mathematician that cannot do on paper what a computer does for him, is not mathematician at all. Using the tool is one thing, relying on it is quite another, especially if you dont understand what is going on behind the scenes.

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  • $\begingroup$ Good points. I would also point out that the OP in this case clearly understands the problem, and is more asking a Mathematica users question than a math question. Same with the people who ask how to do something in MATLAB. It's a good question to ask, since the OP wants to make sure that he isn't blindly relying on the tool. Good points though, I agree with it! :) $\endgroup$ – FundThmCalculus Nov 29 '14 at 4:37

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