Summary: A NOTE ON THE JORDAN CANONICAL FORM
Department of Mathematics and Statistics
King Fahd University of Petroleum & Minerals
Dhahran, Saudi Arabia
A proof of the Jordan canonical form, suitable for a first course in linear
algebra, is given. The proof includes the uniqueness of the number and sizes of
the Jordan blocks. The value of the customary procedure for finding the block
generators is also questioned.
2000 MSC: 15A21.
The Jordan form of linear transformations is an exceeding useful result in all theo-
retical considerations regarding conjugacy classes of matrices, nilpotent orbits and the
Jacobson -Morozov theorem. The author wishes to share a proof of the Jordan form
which he found in connection with a problem in Lie theory. The ideas of the proof
give at the same time the number and sizes of all the blocks. The proof has the added
advantage that the most important parts can be taught in a first course on linear alge-
bra, as soon as basic ideas have been introduced and the invariance of dimensions has
been established. It is thus also a contribution to the teaching of these ideas.