## 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)`