Manuscript Em04-A@2 · Em04-A-v2.tex · section · f5b28abc

Exact vectorized generator

Validated dynamical residual interfaces › Exact vectorized generator · lines 1451–1468

With column-stacking, $vec (A M B) = (B^{T} \otimes A) vec M$ . If $Π_{Δ}$ projects onto diagonal entries, then

\frac{d}{d t} vec R = [- i (I_{N} \otimes h - h^{T} \otimes I_{N}) - γ_{r} I_{N^{2}} - 2 γ_{d} (I_{N^{2}} - Π_{Δ})] vec R .

The matrix-exponential representation is exact but not an execution claim. Storing $S$ requires $N^{2}$ entries; a dense $N^{2} \times N^{2}$ generator need not be stored.

Displayed formulas in this passage

unlabeled · line 1456
$\frac{d}{d t} vec R = [- i (I_{N} \otimes h - h^{T} \otimes I_{N}) - γ_{r} I_{N^{2}} - 2 γ_{d} (I_{N^{2}} - Π_{Δ})] vec R .$