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Linear algebra find the minimal polynomial

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


M: V -> V linear operator st M^2 + 1_v = 0
find the POSSIBILITIES for min. pol. of M^3+2M^2+M+3I_v


Homework Equations





The Attempt at a Solution



using M^2 = -1_v,
i rewrote the operator(?) as
M^3 + M + I_v

i dunno what to do. i guessed min poly to be like x^3-x-1
but what would be other possibilities. i seriously doubt the one i guessed is even correct.

i know that, if min poly is u(x) then u(M) = 0.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618

Homework Statement


M: V -> V linear operator st M^2 + 1_v = 0
find the POSSIBILITIES for min. pol. of M^3+2M^2+M+3I_v


Homework Equations





The Attempt at a Solution



using M^2 = -1_v,
i rewrote the operator(?) as
M^3 + M + I_v

i dunno what to do. i guessed min poly to be like x^3-x-1
but what would be other possibilities. i seriously doubt the one i guessed is even correct.

i know that, if min poly is u(x) then u(M) = 0.
M^3=(-M), isn't it?
 
  • #3
60
0
got it.
 

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