hi all
came across a problem in my homework set which gave 3 eigenvalues and when I worked them through for the eigenvectors I got only 2 unique eigenvectors.
Am i correct to reason that having n eigenvalues does not necessarily translate to n unique eigenvectors?
if so why is this the case?
for completeness, here is the problem:
[1 1 0; 3 3 4;-1 -1 0]
semi colon denotes new row.
we worked down to eigenvalues of 2, 3 and 3 and the vectors being {-1,1,0}, {-1,-1,1}, the later of course coming out twice.
an explanation would be much appreciated!
came across a problem in my homework set which gave 3 eigenvalues and when I worked them through for the eigenvectors I got only 2 unique eigenvectors.
Am i correct to reason that having n eigenvalues does not necessarily translate to n unique eigenvectors?
if so why is this the case?
for completeness, here is the problem:
[1 1 0; 3 3 4;-1 -1 0]
semi colon denotes new row.
we worked down to eigenvalues of 2, 3 and 3 and the vectors being {-1,1,0}, {-1,-1,1}, the later of course coming out twice.
an explanation would be much appreciated!
