On 15 June 2010 13:25, Jason Grout <jason-s...@creativetrax.com> wrote: > On 6/15/10 6:21 AM, Minh Nguyen wrote: > >> >> As you can see, these two characteristic polynomials differ in only >> their signs. One can be obtained from the other by multiplying through >> by -1. What I would like to know is: Is there some reason for this >> inconsistency? Or are the two characteristic polynomials above >> "essentially" the same? >> > > One is computed using x*Id-M, the other by M-x*Id. This will lead to a sign > difference for odd-sized matrices. In my graduate abstract algebra course, > we defined the characteristic polynomial using x*Id-M specifically so that > we'd always have a monic polynomial as the output. >
Sure, though in undergraduate teaching one advantage is using M-x*Id is that they are less likely to make sign errors if they subtract x from the diagonal entries than if they have to negate all entries and add x to the diagonal.... Having said that, I would definitely agree that the *definition" of the char poly should be something monic, even if in practice it may be convenient to work with its negative. John > Jason > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
