Eigenvalues and Eigenvectors Flashcards
1
Q
with the equation AX = LAMDA.X
a. what is the eigenvector ?
b. what is the eigenvalue ?
A
a. X
b. LAMDA
2
Q
how many eigenvalues does a n x n matrix have ?
A
n
3
Q
what are the eigenvalues of A^T
A
they are the same as those of A
4
Q
how do you solve to find the eigenvalues ?
A
AX = LAMDA.X
AX - LAMDA.X.i = 0
(A - i.LAMDA) . X = 0
x = 0
or
(|A - i.LAMDA|) = 0
find a matrix
then take the characteristic polynomial
solve to find the eigenvalues
and sub them into the matrix to find the value
5
Q
what is the characteristic polynomial ?
A
it is the product of the leading diagonal equal to zero ???????????? not sureeeee
6
Q
what is the casey hamilton theory ?
A
the theory that every matrix satisfys its own characteristic polynomial
