#### Triangular Feedback Matrices

An interesting class of feedback matrices, also explored by Jot
[216], is that of *triangular
matrices*. A basic fact from linear algebra
is that triangular matrices (either lower or upper triangular) have
all of their eigenvalues along the diagonal.^{4.13} For example, the
matrix

It is important to note that not all triangular matrices are lossless. For example, consider

One way to avoid ``coupled repeated poles'' of this nature is to use non-repeating eigenvalues. Another is to convert to Jordan canonical form by means of a similarity transformation, zero any off-diagonal elements, and transform back [329].

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Mean Free Path

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Most General Lossless Feedback Matrices