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A change of basis of a matrix is

$$ M'=PMP^{-1} $$

But a vector is

$$ v'=Bv $$

A multivector $u$ can be represented as a matrix, but it is also a vector.

So...

$$ u'=Vu $$

or

$$ u'=VuV^{-1} $$

Is $V$ an arbitrary multivector (provided it has an inverse - thus a general linear group multi-vector...)?

Anon21
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1 Answers1

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I'll assume we are talking about orthonormal basies. Then a change of basis is just a rotation. Rotate each basis vector and you have the new basis.

The computer system I have can't deal with that. The basis in unchangeable. It seems to me that what is needed instead is to transform every element in your space as though it were in the new basis, even though as far as the computer is concerned the basis hasn't changed. That means you apply the inverse of that rotation to every element.

user11865
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  • You don't address the context "Geometric Algebra" which is a domain of its own, with specific concepts, notations, etc. – Jean Marie Feb 15 '23 at 13:18