Direct Determinant expansion

  • Thread starter Grand
  • Start date
  • #1
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Homework Statement


How do I show that det(I+Adt)=1+tr(A)dt +... ? Please help me :)


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
311
1
Write I + A dt = exp(A dt). Then use the property det(exp(A)) = exp(trA). (for dt small)
 
  • #3
311
1
Another way to do it using the determinant formula

[tex]det(A) = \epsilon_{i_1i_2i_3...}A_{i_11}A_{i_22}A_{i_33}...[/tex]

That gives you the same result. Try it!
 

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