In this segment we are talking about some
theorems of corresponding to eigenvalues and
eigenvectors so one of the theorems says as
follows that [A] is a nxn matrix so what that
means is that [A] is a square matrix then
[A] transpose has same eigenvalues as [A]
so what that basically means is that if you
have a square matrix and you are able to find
its eigenvalues then if you take its transpose
then it has the same eigenvalues as the matrix
so lets suppose that somebody says that this
particular matrix right here [A]= 2, -3.5,
6, 3.5, 5, 2, 8, 1, 8.5 and if you take this
particular matrix right here and you find
its eigenvalues by following the procedure
you will get 3 eigenvalues you ll get lambda1=-1.547,
lambda2=12.33, lambda3=4.711 so these are
3 eigenvalues which you are going to get for
that particular matrix so now if somebody
gave me another matrix [B] like this one so
[B]= 2, 3.5, 8, -3.5, 5, 1, 6, 2, 8.5 and
gave me a matrix like this one if I realize
that hey this matrix [B] is simply the transpose
of the [A] matrix as you can see that 2 -3.5
6 is right here 3.5 5 2 is right here 8 1
8.5 is right here so the [B] matrix here is
same as the [A] transpose then the eigenvalues
of [B] are the same so lambda1=-1.547, so
the eigenvalues of [B] lambda2=12.33, lambda3=4.711
and that is the end of this segment
