Jury Table

Theorem

The Jury Test:
Assume $c_n>0$, (if not use $\Delta$*=-1)
Then $\Delta$ is Shur, iff the leading coefficients of $R^i[z]$ for $i\in 0,\dots ,n$ are positive

This is useful because if we have a very high order characteristic polynomial, its hard to factor so its almost impossible to find those roots in Polynomial Time (there is no quintic formula for example).

This is kind of a Pain in the Ass to look at. Trying to put this in words is:

• Each iteration generates an $R^{0+i}$ row and a $Q^{0+i}$ row.
• Each $R$ cell is computed by doing → $\text{matching R cell}-\frac{\text{first Q cell}}{\text{first R cell}}\text{matching Q cell}$
• $Q$ is just $R$ flipped The point of this is that we are recursively reducing the dimensionality of our characteristic polynomial