# clifford.MultiVector¶

class clifford.MultiVector(layout, value=None, string=None, *, dtype: numpy.dtype = <class 'numpy.float64'>)[source]

An element of the algebra

Parameters
• layout (instance of clifford.Layout) – the layout of the algebra

• value (sequence of length layout.gaDims) – the coefficients of the base blades

Notes

The following operators are overloaded:

• A * B : geometric product

• A ^ B : outer product

• A | B : inner product

• A << B : left contraction

• ~M : reversion

• M(N) : grade or subspace projection

• M[N] : blade projection

Attributes

 I Returns a MultiVector that is the pseudoscalar of this space. blades_list ordered list of blades present in this MV even Even part of this multivector odd Odd part of this mulitvector pseudoScalar Returns a MultiVector that is the pseudoscalar of this space.

Methods

 __init__ Constructor. adjoint Adjoint / reversion, $$\tilde M$$ anticommutator The anti-commutator product of two multivectors, $$(MN + NM)/2$$ as_array astype Change the underlying scalar type of this vector. basis Finds a vector basis of this subspace. clean Sets coefficients whose absolute value is < eps to exactly 0. commutator The commutator product of two multivectors. conjugate The Clifford conjugate (reversion and grade involution). dual The dual of the multivector against the given subspace I, $$\tilde M = MI^{-1}$$ exp factorise Factorises a blade into basis vectors and an overall scale. gradeInvol The grade involution of the multivector. grades Return the grades contained in the multivector. inv invPS Returns the inverse of the pseudoscalar of the algebra. isBlade Returns true if multivector is a blade. isScalar Returns true iff self is a scalar. isVersor Returns true if multivector is a versor. join The join of two blades. lc The left-contraction of two multivectors, $$M\rfloor N$$ leftInv Return left-inverse using a computational linear algebra method proposed by Christian Perwass. leftLaInv Return left-inverse using a computational linear algebra method proposed by Christian Perwass. left_complement mag2 Magnitude (modulus) squared, $${|M|}^2$$ meet The meet of two blades. normal Return the (mostly) normalized multivector. normalInv The inverse of itself if $$M \tilde M = |M|^2$$. project Projects the multivector onto the subspace represented by this blade. rightInv Return left-inverse using a computational linear algebra method proposed by Christian Perwass. right_complement round Rounds all coefficients according to Python’s rounding rules. vee Vee product $$A \vee B$$. x The commutator product of two multivectors.