Blades in Clifford Algebra

This page is a sub-page of our page on Clifford Algebra

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The sub-pages of this page are:

• Blades in Geometric Algebra

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Related KMR-pages:

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Other related sources of information:

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Formulas from Ambjörn’s presentation at SIGGRAPH 2000:

\, \mathrm{V}^n \, , \, e_1 \, , e_2 \, , \dots , e_n \,

\, \mathrm{G} = \mathrm{G}_n = \mathrm{G}(\mathrm{V}^n) \,

\, M = \sum\limits_{k = 0}^{n} {\langle \, M \, \rangle}_k \,

\, {\langle \, M \, \rangle}_k = B_1 + B_2 + \cdots \,

\, A_k = a_1 \wedge a_2 \wedge \cdots \wedge a_k \,

\, A_k \neq 0 \, \iff \, \{ a_1, a_2, \dots , a_k \} \,

\, P \in \mathrm{G}_n \,


\, P = p_1 \wedge p_2 \wedge \cdots \wedge p_n \,


\, I = e_1 \wedge e_2 \wedge \cdots \wedge e_n \,

\, [P] = PI^{-1} \,


\, \text{dual}(X) = XI^{-1} \,

\, \text{dual}(X) = X^* \,

\, B = b_1 \wedge b_2 \wedge \cdots \wedge b_m \,

\, \overline{B} \subseteq \mathrm{V}^n \,

\, \overline{B} = \text{Linspan}\{ b_1, b_2, \dots , b_m \} = \,

\, = \text{Linspan}\{ b \in \mathrm{G}_n : b \wedge B = 0 \} \,

\, \{ e_1, \dots , e_m \} \,

\, b_i = \sum\limits_{k = 0}^{m} b_{ik}e_k \; \text{for} \; i = 1, \, \dots \, , m \; , \,

\, B =( \det{b_{ik}}) \, e_1 \wedge e_2 \wedge \cdots \wedge e_m = \,

\, = (\det{b_{ik}}) \, e_1 e_2 \cdots e_m = \,

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