Question

anyone have a quick simple explanation of eigenvalues and eigenvectors?

Answer 1

quick and simple eh, not me. I just started reading up on these myself

Answer 2

the eugne values are of the form:
\[\left|\begin{array}c
\lambda_1&0&0\\
0&\lambda_2&0\\
0&0&\lambda_3\\
\end{array}\right|\]

Answer 3

i think you cross the eugene with the given matrix and solve for a zero determinant

Answer 4

or is it subtract?

Answer 5

Basically an eigenvalue is a number that alters a vector x in the same way as some given matrix A would.\[Ax=\lambda x\]where x is the eigenvector of A and lambda is the eigenvalue of A.
http://tutorial.math.lamar.edu/Classes/LinAlg/EVals_Evects.aspx

Answer 6

\[\left|\begin{array}c
3-\lambda_1&1&2\\
3&5-\lambda_2&3\\
0&1&1-\lambda_3\\
\end{array}\right|\]

Answer 7

right, \[(A-\lambda I)x=0\]then do the determinant and solve for lambda.

Answer 8

but there is only one value lambda amistre, not three. No subscript is needed

Answer 9

taking the determinant gives you a quadratic equation which can be solved for lambda

Answer 10

..... one lambda is definately better to solve than 3 ;)

Answer 11

definately :)

Answer 12

taking the linear algebra next term , yay!!