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I am quite new to Geometric Algebra, this is the reason for the silly question.

In Geometric Algebra, the following implicit definition ofdeterminantis given:

[tex]f(\mathbf{I_n})=det(f)\mathbf{I_n}[/tex]

where f is a linear function extended as an outermorphism, and [tex]\mathbf{I_n}[/tex] is the unit n-blade for [tex]\wedge\mathcal{R}^n[/tex], for example [tex]e_1\wedge\ldots\wedge e_n[/tex]. It is also shown that f can be represented as a square matrix. We also know that in general: [tex]det(A+B)\neq det(A) + det(B)[/tex].

However if we introduce the function [tex]h(X) = f(X)+g(X)[/tex] we have that:

[tex]h(\mathbf{I_n})= f(\mathbf{I_n}) + g(\mathbf{I_n}) = det(h)\mathbf{I_n} = det(f)\mathbf{I_n} + det(g)\mathbf{I_n}[/tex]

We have essentially proved that det(F+G)=det(F)+det(G). There must be a trivial mistake in this: where is it???

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# Determinant of (A+B) in GA: where is the mistake?

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