An n x n matrix A is a defective matrix if it has a defective eigenvalue. Obviously, a Jordan block of dimension greater than 1, and a matrix whose Jordan canonical form has a Jordan block of dimension greater than 1, are defective matrices.

If I am not sure whether what I want to do needs planning permission, how can I find out? You can write to your Local Planning Authority and ask them to give you a ruling (or, as the Act [the Town and Country Planning Act 1947] calls it, a 'determination') whether you need planning permission or not, and if you disagree with their ruling you can appeal to the Minister.

Every category is dual to its own dual, so if a statement holds in all categories so does its dual.

We must accept the imperfectability of the world.