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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 1993 Volume 34, Number 4, Pages 177–183 (Mi smj1642)

An invertibility criterion for multivectors in a real Clifford algebra

P. V. Semenov

Moscow

Abstract: We derive an invertibility criterion for elements of a special type in the classical Clifford algebra $C_n$, namely for elements that are linear combinations of the basic elements $e_\alpha$ of the Clifford algebra $C_n$ with pairwise disjoint nonempty supports a $\alpha\subset\{1,2,\ldots,n\}$. The criteria is of a constructive character and consists in checking a finite number of conditions of linear type on the coefficients of such elements. For lower dimensions $n\le5$ we obtain an invertibility criterion for arbitrary elements of the Clifford algebra $C_n$ (also in terms of coefficients in expansion with respect to the standard basis).

UDC: 512.64:512.552

Received: 25.12.1991


 English version:
Siberian Mathematical Journal, 1993, 34:4, 749–754

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