Universal Similarity Factorization Equalities over Generalized Clifford Algebras

Yong Ge Tian
February 2006
Acta Mathematica Sinica;Feb2006, Vol. 22 Issue 1, p289
Academic Journal
For any element a in a generalized 2 n –dimensional Clifford algebra $${\fancyscript C}$$ ℓ n ( $${\Bbb F}$$ ) over an arbitrary field $${\Bbb F}$$ of characteristic not equal to two, it is shown that there exits a universal invertible matrix P n over $${\fancyscript C}$$ ℓ n ( $${\Bbb F}$$ ) such that $$ P^{{ - 1}}_{n} D_{a} P_{n} = \phi {\left( a \right)} \in F^{{2^{n} \times 2^{n} }} $$ , where ϕ( a) is a matrix representation of a over and D a is a diagonal matrix consisting of a or its conjugate.


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