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\mathbf{A1}=\lambda\mathbf1
</math>
where the condition that <math>\mathbf A</math> has <math>\mathbf1</math> as an eigenvector ensures invertibility by sidestepping the information loss due to the invariance: <math>\operatorname{softmax}(\mathbf x+\alpha\mathbf1)=\operatorname{softmax}(\mathbf x)</math>. Note in particular that <math>\mathbf A=\lambda\mathbf I_n</math> is the ''only'' allowed diagonal parametrization, in which case (for <math>\lambda>0</math>) we recover <math>f_\text{cal}(\mathbf p;\lambda^{-1},\mathbf c)</math>, while (for <math>n>2</math>) generalization ''is'' possible with non-diagonal matrices. The '''inverse''' is:
:<math>
\mathbf p = f_\text{gcal}^{-1}(\mathbf q;\mathbf A, \mathbf c)
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