A is a square matrix over F field

if k is the eigen value of A

prove that k is eigen value of A^t too

and has the same eigen vectors

??

eigen vectors are the solution space P(A)

is found by solving (A-kI)x=0

dim P(A)=dim n -dim (ro(a))

rho(a)=rho(a^t)

|A|=|A^t|

these are the laws i maneged to come up with to solve it

??