>>14296400>Ok so its a vector space with a "quadratic form". Thats just mathemathese for an inner product?A quadratic form is a mapping from the vector space to its field that is quadratic, i.e. Q(kx) = k^2Q(x) where k is a scalar and x is an element of the vector space. Equivalently you can think of it as a polynomial over some variables where every term is degree 2 (think of the variables as basis vectors of the vector space).
>Unital algebraYeah it's just an algebra with a multiplicative identity
The Clifford algebra is an algebra where the product of any element with itself is equal to the given quadratic form Q on that element times the identity element.
vv = v^2 = Q(v)
This is its only defined property. For instance, we don't identify the product of two elements v and w with anything, we just write "vw".
You can derive all sorts of properties from this basic definition, here's a basic example. Consider:
(v+w)(v+w) = v^2 + vw + wv + w^2
We then have
vw + wv = {v,w} = Q(v+w) - Q(v) - Q(w)
So now we know how the elements behave under commutation.
