- #1
spaghetti3451
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Homework Statement
Find the eigenvalues and eigenvectors of the following matrix: M =
1 1
0 1
Can this matrix be diagonalised?
Homework Equations
The Attempt at a Solution
The characteristic equation is [itex](1 - \lambda)^{2} = 0[/itex] which gives [itex]\lambda = 1[/itex]. Substitute [itex]\lambda = 1[/itex] and eigenvector = {x,y} into the eigenvalue equation gives the two equations x+y = x and y = y. The first equation implies that y = 0. The second equation is redundant. So, x is free to assume any complex value. So, the eigenvalue is 1 and the eigenvector is {1,0}.
I think everything I have done so far is fine. If it isn't, please point out.
The problem starts with the second part: 'Can this matrix be diagonalised?' I know that to diagonalise a matrix is equivalent to changing the basis of the matrix and the eigenvectors. I am not quite sure I get this or the fact that the eigenvectors have to span the ? to accomplish the diagonalisation.
Thanks in advance for any help.