linearalgebra
Interface VectorSpaceInterface

All Known Implementing Classes:
VectorSpace

public interface VectorSpaceInterface


Method Summary
 boolean areIndependentColumns()
          Returns true if all non-trivial combinations of all column vectors are non-zero.
 boolean areOrthogonalColumns()
           
 int[] getBasisColumns()
          Returns the columns for the column basis
 int getColumnCount()
          Returns the number of column vectors used to define this space.
 VectorSpaceInterface getColumnSpace()
          A basis for a vector space is the set of column vectors such that all vectors are linearly independent and the set spans the space.
 VectorInterface getColumnVector(int colIndex)
          Returns one of the column vectors of the space.
 int getDimension()
          All bases of this space have the same number of vectors.
 VectorSpaceInterface getLeftNullspace()
           
 NumericMatrixInterface getMatrix()
           
 VectorSpaceInterface getNullspace()
           
 int getRank()
          Returns the number of non-zero pivots in U after the system A describing the vector space has been factored into A=LU.
 VectorSpaceInterface getRowSpace()
          Returns the space spanned by all of the rows
 VectorSpaceInterface getSubspace(VectorInterface v)
           
 boolean hasExistence()
          There is 1 to infinite solutions.
 boolean hasUniqueness()
          There is 0 or 1 solution At most one solution.
 boolean isInconsistent()
          For the system ax=b describing this space, if a=0 and b!=0 there are an zero number of solutions.
 boolean isMember(NumericVectorInterface v)
          The space is defined by the system ax=b.
 boolean isNonsingular()
          For the system ax=b that describes the space, return true if a!=0.
 boolean isOrthogonal(VectorSpaceInterface vs)
           
 boolean isSubspace(VectorSpaceInterface v)
          Returns true if all vectors in v are contained in this space.
 boolean isUnderdetermined()
          For the system ax=b describing this space, if a=0 and b=0 there are an infinite number of solutions.
 boolean normalizeColumns()
           
 boolean spansSpace(VectorSpaceInterface v)
          Checks if all of the vectors in v can be described by a linear combination of the vectors in this space.
 

Method Detail

getMatrix

NumericMatrixInterface getMatrix()

getSubspace

VectorSpaceInterface getSubspace(VectorInterface v)

spansSpace

boolean spansSpace(VectorSpaceInterface v)
Checks if all of the vectors in v can be described by a linear combination of the vectors in this space. If so, then v spans this.

Parameters:
v - A vector space that may span this space.
Returns:
Returns true if v spans this space. Returns false otherwise.

isMember

boolean isMember(NumericVectorInterface v)
The space is defined by the system ax=b. Returns true if a solution exists for ax=v meaning v is located in the hyper-plane defined by this space. Returns false otherwise.

Parameters:
v - The vector to check for membership.

isSubspace

boolean isSubspace(VectorSpaceInterface v)
Returns true if all vectors in v are contained in this space.

Parameters:
v -

getRank

int getRank()
Returns the number of non-zero pivots in U after the system A describing the vector space has been factored into A=LU.


getDimension

int getDimension()
All bases of this space have the same number of vectors. This number is called the degree of freedom, or the dimension, of the space. Note that this is a different concept than the dimension of a vector.


getColumnCount

int getColumnCount()
Returns the number of column vectors used to define this space. This number may change as the space is manipulated.


getColumnVector

VectorInterface getColumnVector(int colIndex)
Returns one of the column vectors of the space.

Parameters:
colIndex -

isNonsingular

boolean isNonsingular()
For the system ax=b that describes the space, return true if a!=0. There exists a single solution to ax=b. Returns false otherwise.


isUnderdetermined

boolean isUnderdetermined()
For the system ax=b describing this space, if a=0 and b=0 there are an infinite number of solutions. Any x satisfies 0x=0.


isInconsistent

boolean isInconsistent()
For the system ax=b describing this space, if a=0 and b!=0 there are an zero number of solutions. No x satisfies 0x=b.


areIndependentColumns

boolean areIndependentColumns()
Returns true if all non-trivial combinations of all column vectors are non-zero.


areOrthogonalColumns

boolean areOrthogonalColumns()

normalizeColumns

boolean normalizeColumns()

getColumnSpace

VectorSpaceInterface getColumnSpace()
A basis for a vector space is the set of column vectors such that all vectors are linearly independent and the set spans the space.


getRowSpace

VectorSpaceInterface getRowSpace()
Returns the space spanned by all of the rows


getBasisColumns

int[] getBasisColumns()
Returns the columns for the column basis


getNullspace

VectorSpaceInterface getNullspace()

getLeftNullspace

VectorSpaceInterface getLeftNullspace()

hasExistence

boolean hasExistence()
There is 1 to infinite solutions. At least one solution.


hasUniqueness

boolean hasUniqueness()
There is 0 or 1 solution At most one solution.


isOrthogonal

boolean isOrthogonal(VectorSpaceInterface vs)