Just as a recap, eigenvectors are the vectors that does not change its orientation, but just scales by a factor of its corresponding eigenvalue. To
The eigenvectors with eigenvalue λ,if any, are the nonzero solutions of the equation Av=λv. We can rewrite this equation as follows: Av=λv⇐⇒Av−λv=0⇐⇒Av−λInv=0⇐⇒(A−λIn)v=0.
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The eigenvalues are scalar quantities, , where the determinant of is equal to zero. First, find an expression for the determinant: Now set this equal to zero, and solve: this can be factored (or solved in another way) The eigenvalues are -5
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A100 was found by using the eigenvalues of A, not by multiplying 100 matrices. Those eigenvalues (here they are 1 and 1=2) are a new way to see into the heart of a matrix. To
These are also called eigenvectors of A, because A is just really the matrix representation of the transformation. So in this case, this would be an eigenvector of A, and this would be the eigenvalue