AbstractVector

Extension

Create new vector from a n-tuple of real numbers. Dimension of the vector is determined by the amount of numbers.RealVector[1.2,0.3,5.6,3.2]

Applies the gramSchmidt process to the vectors and returns an array of orthogonal vectors that span the same subspace as the original vectors.

components for vectors up to 3 dimensions.RealVector[1,2,3].x

inner product.RealVector[1,2,3]<|>RealVector[2,5,7] ComplexVector[Complex(1,0),Complex(1,2)]<|>ComplexVector[Complex(1,3),Complex(0,2)] // the canonical base in R^N is orthogonal 3.collect{ |i| RealVector.canonB(i, 3)<|>RealVector.canonB((i+1).mod(3), 3) };

distance.RealVector[1,2,3].dist(RealVector[2,5,7]) ComplexVector[Complex(1,0),Complex(1,2)].dist(ComplexVector[Complex(1,3),Complex(0,2)])

euclidian norm - sqrt( vector <|> vector ).RealVector[0,2,0].norm ComplexVector[Complex(1,0),Complex(1,2)].norm

RealVector[7,2,3].normalize.norm ComplexVector[Complex(1,0),Complex(1,2)].normalize.norm

RealVector[0,0,1,0].isOrthogonal(RealVector[1,0,0,0]) ComplexVector[Complex(1,0),Complex(0,2)].isOrthogonal(ComplexVector[Complex(0,3),Complex(0,2)])

returns the transposed vector as a one row matrix.RealVector[0,0,1,0].transpose

projects vector into the current vector.RealVector[0,0,1].proj(RealVector[3.2,5.6,3.6])

Clips a vector in all dimensions.

Arguments: