nilpotent matrix

The trace of any power of a nilpotent matrix is zero.

Every singular matrix can be written as a product of nilpotent matrices.

Though the examples above have a large number of zero entries, a typical nilpotent matrix does not.

One example of a nilpotent element is a nilpotent matrix.

See nilpotent matrix for more.

Thus, a linear map is nilpotent iff it has a nilpotent matrix in some basis.

Some matrices are not diagonalizable over any field, most notably nonzero nilpotent matrices.

This matrix is nilpotent with degree n, and is the "canonical" nilpotent matrix.

Nilpotent matrices with complex entries form the main motivating case for the general theory, corresponding to the complex general linear group.

Nilpotent matrix and nilpotent transformation on PlanetMath.

The dominance ordering determines the inclusions between the Zariski closures of the conjugacy classes of nilpotent matrices.

In mathematics, nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple Lie groups and semisimple Lie algebras.

A useful form of the theorem says that if a Lie algebra L of matrices consists of nilpotent matrices, then they can all be simultaneously brought to a strictly upper triangular form.

The degree of an n x n nilpotent matrix is always less than or equal to n. For example, every 2 x 2 nilpotent matrix squares to zero.