Difference between revisions of "Talk:Aufgaben:Problem 4"
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Did we have \(det(e^{tA}) = e^{tr(A)}\) in the lecture? [[User:Carl|Carl]] ([[User talk:Carl|talk]]) 23:51, 19 June 2015 (CEST) | Did we have \(det(e^{tA}) = e^{tr(A)}\) in the lecture? [[User:Carl|Carl]] ([[User talk:Carl|talk]]) 23:51, 19 June 2015 (CEST) | ||
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| + | Well actually it's \(det(e^{tA}) = e^{tr(tA)} = e^{t\cdot tr(A)}\). | ||
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| + | The first equality is a property of the matrix exponential, see Wikipedia: [[https://en.wikipedia.org/wiki/Matrix_exponential#The_determinant_of_the_matrix_exponential]] and Trubo used that property too in the lectures. | ||
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| + | The second equality follows from the linearity of the trace. So I don't see any problems on using that. | ||
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| + | [[User:Djanine|Djanine]] ([[User talk:Djanine|talk]]) 11:10, 22 June 2015 (CEST) | ||
Revision as of 09:10, 22 June 2015
Did we have \(det(e^{tA}) = e^{tr(A)}\) in the lecture? Carl (talk) 23:51, 19 June 2015 (CEST)
Well actually it's \(det(e^{tA}) = e^{tr(tA)} = e^{t\cdot tr(A)}\).
The first equality is a property of the matrix exponential, see Wikipedia: [[1]] and Trubo used that property too in the lectures.
The second equality follows from the linearity of the trace. So I don't see any problems on using that.
