# Class Basis

All Implemented Interfaces:
SparseStructure, Vector, AbelianGroup<Vector>, BanachSpace<Vector,Real>, HilbertSpace<Vector,Real>, VectorSpace<Vector,Real>, DeepCopyable, Iterable<SparseVector.Entry>

public class Basis extends SparseVector
A basis is a set of linearly independent vectors spanning a vector space. Every element in this space can be uniquely represented by a linear combination of elements in the basis. This implementation is the standard basis of the Euclidean Rn space.

## Nested classes/interfaces inherited from class dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse.SparseVector

SparseVector.Entry, SparseVector.Iterator
• ## Constructor Summary

Constructors
Constructor
Description
Basis(int dim, int i)
Construct a vector that corresponds to the i-th dimension in Rn.
• ## Method Summary

Modifier and Type
Method
Description
static List<Vector>
getBasis(int dim)
Get the full set of the standard basis vectors.
static List<Vector>
getBasis(int dim, int nCols)
Get a subset of the standard basis vectors.

### Methods inherited from class dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse.SparseVector

add, add, add, angle, deepCopy, divide, equals, get, hashCode, innerProduct, innerProduct, iterator, leftMultiply, minus, minus, minus, multiply, multiply, nNonZeros, norm, norm, opposite, pow, scaled, scaled, set, size, toArray, toString, ZERO

### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

### Methods inherited from interface java.lang.Iterable

forEach, spliterator
• ## Constructor Details

• ### Basis

public Basis(int dim, int i)
Construct a vector that corresponds to the i-th dimension in Rn. That is (a 1 in the i-th entry), $\begin{bmatrix} 0\\ ...\\ 1\\ ...\\ 0 \end{bmatrix}$
Parameters:
dim - the dimension
i - the i-th dimension in Rn
• ## Method Details

• ### getBasis

public static  getBasis(int dim)
Get the full set of the standard basis vectors.
Parameters:
dim - the dimension
Returns:
the basis vectors
• ### getBasis

public static  getBasis(int dim, int nCols)
Get a subset of the standard basis vectors.
Parameters:
dim - the dimension
nCols - the number of basis vectors requested; it must be smaller than dim
Returns:
the basis vectors
Throws:
IllegalArgumentException - if there are more columns requested than the dimension