- #1
gopi9
- 14
- 0
Hi everyone,
I have two matrices A and B,
A=[0 0 1 0; 0 0 0 1; a b a b; c d c d] and B=[0 0 0 0; 0 0 0 0; 0 0 a b; 0 0 c d].
I have to proves theoretically that two of the eigenvalues of A and B are equal and remaining two eigenvalues of A are 1,1.
I tried it by calculating the determinant of A and B and I got close to the result but I am not able to prove it completely.
I got result like this,
sum of roots of determinant of A and B as
p+q+r+s=p1+q1 (p,q,r,s are roots of det of A, p1,q1 are roots of det of B)
Product of roots
p*q*r*s=p1*q1
pqr+qrs+prs+pqs=-2(p1*q1).
Please help me to show that two eigenvalues of A and B are equal.
Thanks.
I have two matrices A and B,
A=[0 0 1 0; 0 0 0 1; a b a b; c d c d] and B=[0 0 0 0; 0 0 0 0; 0 0 a b; 0 0 c d].
I have to proves theoretically that two of the eigenvalues of A and B are equal and remaining two eigenvalues of A are 1,1.
I tried it by calculating the determinant of A and B and I got close to the result but I am not able to prove it completely.
I got result like this,
sum of roots of determinant of A and B as
p+q+r+s=p1+q1 (p,q,r,s are roots of det of A, p1,q1 are roots of det of B)
Product of roots
p*q*r*s=p1*q1
pqr+qrs+prs+pqs=-2(p1*q1).
Please help me to show that two eigenvalues of A and B are equal.
Thanks.