#### Most General Lossless Feedback Matrices

As shown in §C.15.3, an FDN feedback matrix is lossless if and only if its eigenvalues have modulus 1 and its eigenvectors are linearly independent.A

*unitary matrix*is any (complex) matrix that is inverted by its own (conjugate) transpose:

*Hermitian conjugate*(

*i.e.*, the complex-conjugate transpose) of . When is real (as opposed to complex), we may simply call it an

*orthogonal matrix*, and we write , where denotes matrix transposition. All unitary (and orthogonal) matrices have unit-modulus eigenvalues and linearly independent eigenvectors. As a result, when used as a feedback matrix in an FDN, the resulting FDN will be lossless (until the delay-line damping filters are inserted, as discussed in §3.7.4 below).

**Next Section:**

Triangular Feedback Matrices

**Previous Section:**

Householder Reflections