Consider the matrix

 

Find the Eigenvalues of the matrix A. 

Find two (linearly independent) eigenvectors for this matrix. 

Show that the two eigenvectors are perpendicular (by showing that their Inner product. r+ r = 0). 

Find a similarity transformation, C, that will diagonally the matrix A (form the matrix C by normalizing the two eigenvectors and then using one of the normalized eigenvectors as the first column and the second normalized eigenvector as the second column).

Show that the matrix C is Unitary.

Transcribed Image Text:

A= (2 2 -1 A= (2 2 -1

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Finding the eigenvalues of A To find the eigenvalues of A we solve the characteristic equation detA I 0 This gives us the quadratic equation 2 2 1 0 T... View the full answer