This is known to be hard to compute for large matrices.

For such matrices, the half-vectorization is sometimes more useful than the vectorization.

Similar statements can be made for negative definite and semi-definite matrices.

The table at the right shows two possibilities for 2-by-2 matrices.

The result provides a simple framework to understand various canonical form results for square matrices over fields.

However, this is often impossible for larger matrices, in which case we must use a numerical method.

A definition for matrices over a ring K (such as integers) is also possible.

This theorem is a special case of the Jordan canonical form for matrices.

The cofactor equation listed above yields the following result for 2x2 matrices.

For general matrices, the operator norm is often difficult to calculate.