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The Cell Method by Elena Ferretti

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CHAPTER 2

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ALGEBRA AND THE GEOMETRIC INTERPRETATION OF VECTOR SPACES

In order to deepen the mathematical foundations of the cell method (CM), in this chapter we introduce some basics of exterior algebra (Section 2.1) and geometric algebra (Section 2.2), the two fundamental settings for the geometric study of vector spaces. Of special importance for the philosophy of the CM are the geometric interpretations of the operations on vectors, provided by both the exterior and geometric algebra, and the notions of extension of a vector by another vector, multivector (or p-vector), dual vector space, bialgebra, and covector. The geometric approach allows ...

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