In Wikipedia It is written that

Jordan canonical form is an upper triangualr matrix of a particular form called a Jordan matrix representing a linear operator on a finite dimensional vector space with respect to some basis enter image description here

My confusion :why is lower triangular matrix not mentioned in the Jordan normal form definition ?

My thinking : I can also construct lower triangular matrix in the same pattern

see the diagram below

enter image description here


1 Answer 1


Every matrix is simlar to its transponse, so a lower triangular Jordan block would be similar to an upper triangular Jordan block. I recall reading a linear algebra book (I think Serge Lang's) where the Jordan form was lower triangular. It's all a matter of reversing the order of the cyclic (sub-)basis.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.