- #1
Robb
- 225
- 8
Homework Statement
Show that A is a scalar matrix kI if and only if the minimum polynomial of A is m(t) = t-k
Homework Equations
The Attempt at a Solution
f(A) is monic
f(A) = 0 since A = kI
Next we must show that deg(g) < deg(f)
I guess I'm not sure where g comes from. Is it merely an assumption? I assume g is a polynomial with root A.
And, if deg(g) < deg(f) then deg(g) must be 0 because deg(f) is 1 so g must be a constant. I think I'm just having trouble wrapping my mind around g. Please advise.