Ruby

# Properties of vectors:

# * Vector.independent?(*vs)

# * #independent?(*vs)

#

# PROPERTIES -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

#++

#

# Returns +true+ iff all of vectors are linearly independent.

#

# Vector.independent?(Vector[1,0], Vector[0,1])

# => true

#

# Vector.independent?(Vector[1,2], Vector[2,4])

# => false

#

def Vector.independent?(*vs)

vs.each do |v|

raise TypeError, "expected Vector, got #{v.class}" unless v.is_a?(Vector)

Vector.Raise ErrDimensionMismatch unless v.size == vs.first.size

end

return false if vs.count > vs.first.size

Matrix[*vs].rank.eql?(vs.count)

end

#

# Returns +true+ iff all of vectors are linearly independent.

#

# Vector[1,0].independent?(Vector[0,1])

# => true

#

# Vector[1,2].independent?(Vector[2,4])

# => false

#

def independent?(*vs)

self.class.independent?(self, *vs)

end

#--