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May 7th, 2013, 06:07 AM  #1 
Newbie Joined: May 2013 Posts: 3 Thanks: 0  With characteristic polynomial show that A is invertible Show that square matrix [itex]A[/latex] is reversible if [itex]p_{A}(0)\neq 0[/latex] where [itex]p_{A}[/latex] is characteristic polynomial. Prove similar statement for minimal polynomial. The first part should be very similar to this (if not completely correct?): If [itex]A[/latex] is reversible than [itex]detA\neq 0[/latex]. Characteristic polynomial is by it's definition calculated as . for than: but is reversible and therefore so . End of part one (the other direction is similar). Part two: Minimal polynomial: For minimal polynomial but I am not sure how to continue.. BTW, why would this differ from the first part at all? could easily also be minimal? If in characteristic polynomial I insert instead of : but I don't see how this proves that is reversible. Could somebody give ma hint what's the whole idea here? :/ Thanks for all the help! This is actually Home Work I have to do so if there is a separated topic for this kind of questions I sincerely apologize! 
May 7th, 2013, 06:09 AM  #2  
Newbie Joined: May 2013 Posts: 3 Thanks: 0  Re: With characteristic polynomial show that A is invertible
SORRY for the mistakes in first post: Quote:
 
May 17th, 2013, 04:04 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: With characteristic polynomial show that A is invertible
Don't insert "A" or (that doesn't really make sense, is a number, not a matrix), insert . In that case becomes , exactly what you want.


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