AbstractVector an element of F^N.

Inherits from: Object : Collection : SequenceableCollection : ArrayedCollection : AbstractVector

Represents an element of F^N, where F is either the real numbers R or the complex numbers C.  Usual operations are implemented. Examples are given with RealVector.

Creation / Class Methods

*new (args)

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]

*gramSchmidt (vectors)

Applies the gramSchmidt process to the vectors and returns an array of orthogonal vectors that span the same subspace as the original vectors. Note: rounding erros will usually not give you completely orthogonal vectors.

a = RealVector[1,2];

b = RealVector[3,4];

c = RealVector.gramSchmidt([a,b])

c[0]<|>c[1]

Accessing Instance and Class Variables

x,y,z

components for vectors up to 3 dimensions.

RealVector[1,2,3].x

<|> (vector)

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) };

dist (vector)

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)])

norm

euclidian norm -  sqrt( vector <|> vector ).

RealVector[0,2,0].norm

ComplexVector[Complex(1,0),Complex(1,2)].norm

normalize

RealVector[7,2,3].normalize.norm

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

isOrthogonal (vector)

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)])

usual vector space operations

RealVector[1,2,3] + RealVector[4,5,6]

RealVector[1,2,3]*2

ComplexVector[Complex(1,0),Complex(0,2)]+ComplexVector[Complex(0,3),Complex(0,2)]

ComplexVector[Complex(1,0),Complex(0,2)]*Complex(1,2)

transpose

returns the transposed vector as a one row matrix.

RealVector[0,0,1,0].transpose

proj (vector)

projects vector into the current vector.

RealVector[0,0,1].proj(RealVector[3.2,5.6,3.6])