What does the degree of a matrix minimal polynomial encode?
Solution 1:
If $A$ has distinct $n$ non-zero eigen values in an extension field of $F$, $\mu$ is the characteristic polynomial of $A$. Hence deg $\mu = n =$ rank $A$.
What does the degree of a matrix minimal polynomial encode?
Solution 1:
If $A$ has distinct $n$ non-zero eigen values in an extension field of $F$, $\mu$ is the characteristic polynomial of $A$. Hence deg $\mu = n =$ rank $A$.