We are looking for a vector x such that x and Ax point in the same direction. But the length can change, the length is scaled by λ
The characteristic polynomial of an n by n matrix A is the nth degree poly- nomial det(A − λI) > The roots of this polynomial are the eigenvalues of A. > > The constant term (the coefficient of λ0) is the determinant of A. > > • The coefficient of λn−1 term is the trace of A. > > • The other coefficients of this polynomial are more complicated invariants > of the matrix A. > See further: M.I.T. 18.03 Ordinary Differential Equations 18.03 Extra Notes and Exercises ⃝c Haynes Miller, David Jerison, Jennifer French and M.I.T., 2013 > On Mar 2, 2023, at 9:23 PM, Michal Wallace <[email protected]> wrote: > > Okay, I'm wrong. Sorry. :D > > Yes, the lab gives pretty much my exact example, but they write it like > this: > > viewmat |.j.~/~i:10 > > > My expectations were off because the default table piped through viewmat > doesn't put the numbers in the same positions they would actually occupy on > the plane. > > > > On Thu, Mar 2, 2023 at 9:33 AM Jan-Pieter Jacobs <[email protected]> > wrote: > >> I think Esa is right. >> It's explained with some examples in the viewmat lab, pages 8/20-12/20. >> >> It does not seem to work on Android though, just returning a blank window >> (while viewmat on real inputs works perfectly). >> >> On the J Playground, it ddes not work either: it just shows the magnitude, >> but not the arrows. Jios 903.1 gives the same result (i.e. colours, but not >> arrows). >> >> Jan-Pieter >> >> On Thu, 2 Mar 2023, 14:02 esal, <[email protected]> wrote: >> >>> I think it represents the angle (phase, argument) of the complex number >>> while the color is mapped to the magnitude (absolute value, length). >>> >>> Esa >>> >>> On Wed, Mar 1, 2023 at 7:21 PM Michal Wallace <[email protected]> >>> wrote: >>> >>>> What is the word for what the arrows mean in viewmat when you are >> looking >>>> at complex numbers? >>>> >>>> I think that multiplying a number by the arrow's corresponding point is >>>> going to do some kind of shearing (?) in that direction, but can >> someone >>>> help me put this concept into words? >>>> >>>> Thanks! >>>> -Michal >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
