How do we know if we can use power iteration in a given matrix?
$begingroup$
I am trying to understand methods of computing eigenvectors other than using the characteristic polynomial and then using row reduction.
Wikipedia says that power iteration requires that the matrix for which we wish to compute eigenvalues must be diagonalisable.
Am I right in suggesting that diagobalisable means that it does not have an eigenvalue with algebraic multiplicity greater than geometric multiplicity?
If so, how can we tell if we can use power iteration on a matrix (how do we know that it is diagobalisable) without already knowing it’s eigenevectors? Will this method still work if the matrix does not have a dominant eigenvalue?
Thanks for your help.
linear-algebra eigenvalues-eigenvectors
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
$endgroup$
add a comment |
$begingroup$
I am trying to understand methods of computing eigenvectors other than using the characteristic polynomial and then using row reduction.
Wikipedia says that power iteration requires that the matrix for which we wish to compute eigenvalues must be diagonalisable.
Am I right in suggesting that diagobalisable means that it does not have an eigenvalue with algebraic multiplicity greater than geometric multiplicity?
If so, how can we tell if we can use power iteration on a matrix (how do we know that it is diagobalisable) without already knowing it’s eigenevectors? Will this method still work if the matrix does not have a dominant eigenvalue?
Thanks for your help.
linear-algebra eigenvalues-eigenvectors
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
$endgroup$
add a comment |
$begingroup$
I am trying to understand methods of computing eigenvectors other than using the characteristic polynomial and then using row reduction.
Wikipedia says that power iteration requires that the matrix for which we wish to compute eigenvalues must be diagonalisable.
Am I right in suggesting that diagobalisable means that it does not have an eigenvalue with algebraic multiplicity greater than geometric multiplicity?
If so, how can we tell if we can use power iteration on a matrix (how do we know that it is diagobalisable) without already knowing it’s eigenevectors? Will this method still work if the matrix does not have a dominant eigenvalue?
Thanks for your help.
linear-algebra eigenvalues-eigenvectors
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
$endgroup$
I am trying to understand methods of computing eigenvectors other than using the characteristic polynomial and then using row reduction.
Wikipedia says that power iteration requires that the matrix for which we wish to compute eigenvalues must be diagonalisable.
Am I right in suggesting that diagobalisable means that it does not have an eigenvalue with algebraic multiplicity greater than geometric multiplicity?
If so, how can we tell if we can use power iteration on a matrix (how do we know that it is diagobalisable) without already knowing it’s eigenevectors? Will this method still work if the matrix does not have a dominant eigenvalue?
Thanks for your help.
linear-algebra eigenvalues-eigenvectors
linear-algebra eigenvalues-eigenvectors
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
asked Dec 19 '18 at 6:11
AndrewAndrew
357213
357213
add a comment |
add a comment |
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