Hi,(adsbygoogle = window.adsbygoogle || []).push({});

Why is it that if A is m×n-matrix and B is n×m matrices such that m<n, then AB is m×m and BA is n×n matrix. Then the following is true:

pAB(t) = t^(m-n)*pBA(t)

where pAB(t) and pBA(t) are characteristic polynomials of AB and BA

thanks

**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!

# Property of characteristic polynomial

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