Another ( closely related ) method if the field is algebraically closed is to work with the Jordan form of " X ".
12.
This means that one may use Jordan forms that only exist over a larger field to determine whether the given matrices are similar.
13.
I need a relatively simple procedure or algorithm for my purpose i . e . upper triangular but need not be a Jordan form.
14.
Shay and Jordan form a sort of romantic relationship which is cut short when Shay finds out Wade is trying to back out their arrangement.
15.
But this actually gives a clue : somehow the result above holds because of the simplicity of geometry, and a Jordan form doesn't capture geometry.
16.
The various admissible matrix types, called Jordan forms cannot all occur, as the energy conditions that the energy momentum tensor is forced to satisfy rule out certain forms.
17.
Given a complex square matrix A, find a matrix P such that P-1 AP is an upper triangular matrix ( nothing more, need not be a Jordan form ).
18.
Not all matrices are diagonalizable, but at least over the complex numbers ( or any algebraically closed field ), every matrix is similar to a matrix in Jordan form.
19.
Put in another way, a matrix is diagonalizable if each block in its Jordan form has no nilpotent part; i . e ., each " block " is a one-by-one matrix.
20.
:The way I see it is : if N is any nilpotent nxn matrix, then N n = 0 ( because of the normal form of nilpotent matrices, which is just their Jordan form.
