(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose A is a 2x2 real matrix with characteristic polynomial f(t) = t^{2}- 5t +4. Find a real polynomial g(t) of degree 1 such that (g(A))^{2}= A.

Suppose A is a 2x2 complex matrix with A^{2}≠ O. Show that there is a complex polynomial g(t) of degree 1 such that (g(A))^{2}= A.

2. Relevant equations

Cayley-Hamilton Theorem

3. The attempt at a solution

I found that det A = 4 and from f(A) = 0, I found the inverse of A to be 1/4 * A(A-5).

I am completely stuck after this. I let A be a matrix of 4 variables a, b, c, and d, then tried to solve for the variables but ended up with really long and messy terms.

Can someone give me a lead as to what the g(t) has to do with f(t)?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Characteristic Polynomials

**Physics Forums | Science Articles, Homework Help, Discussion**