Let be a finite dimensional vector space over . Let be a linear transformation

on all of whose eigenvalues are zero. Show that for some , i.e.

that is nilpotent.

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- Apr 21st 2010, 11:37 AMJJMC89[SOLVED] Linear Algebra, Nilpotent
Let be a finite dimensional vector space over . Let be a linear transformation

on all of whose eigenvalues are zero. Show that for some , i.e.

that is nilpotent. - Apr 21st 2010, 12:22 PMDefunkt
- Apr 21st 2010, 02:35 PMdwsmith
- Apr 21st 2010, 03:30 PMDefunkt
- Apr 21st 2010, 07:12 PMJJMC89
- Apr 22nd 2010, 04:35 AMHallsofIvy
Well, then you have it, don't you? If all eigenvalues are 0, then the characteristic equation is and every matrix satisfies its own characteristic equation.