= Goldstino null vector with F-term and D-term breaking
{title2=$\mathcal M(F,D/\sqrt2)^T=0$}
For canonical global <four-dimensional N=1 supersymmetry>, define $F^i=\overline{W_i}$, $H_{ij}=W_{ij}$ and $G_{ia}=g^a\bar\phi_j(T^a)^j{}_i$ at a stationary vacuum. <Gauge invariance> of the <superpotential> gives $G^TF=0$, while stationarity of $V=\sum_i|W_i|^2+\frac12\sum_a(D^a)^2$ gives $HF-GD=0$. Therefore the canonically normalized <fermion mass matrix>, after a harmless <gaugino> phase choice, obeys
$$
\begin{pmatrix}H&-\sqrt2G\\-\sqrt2G^T&0\end{pmatrix}\begin{pmatrix}F\\D/\sqrt2\end{pmatrix}=0.
$$
If <supersymmetry> is broken, this vector is nonzero and specifies a massless <Goldstino>. The matrix with off-diagonal blocks $-G$ instead acts on $(F,D)$; it is related to the canonical matrix by a change of normalization, not by equality of canonical entries. Additional zero modes can coexist with the <Goldstino>.
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