Class SubSpace

java.lang.Object
org.flag4j.linalg.SubSpace
public final class SubSpace extends Object
This class contains several methods for computing the subspace of a matrix.

  • Method Details

    • getColSpace

      public static Matrix getColSpace(Matrix src)
      Computes an orthonormal basis of the column space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the column space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the column space of the src matrix.

    • getRowSpace

      public static Matrix getRowSpace(Matrix src)
      Computes an orthonormal basis of the row space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the row space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the row space of the src matrix.

    • getNullSpace

      public static Matrix getNullSpace(Matrix src)
      Computes an orthonormal basis of the null space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the null space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the null space of the src matrix.

    • getLeftNullSpace

      public static Matrix getLeftNullSpace(Matrix src)
      Computes an orthonormal basis of the left null space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the left null space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the left null space of the src matrix.

    • getColSpace

      public static CMatrix getColSpace(CMatrix src)
      Computes an orthonormal basis of the column space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the column space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the column space of the src matrix.

    • getRowSpace

      public static CMatrix getRowSpace(CMatrix src)
      Computes an orthonormal basis of the row space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the row space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the row space of the src matrix.

    • getNullSpace

      public static CMatrix getNullSpace(CMatrix src)
      Computes an orthonormal basis of the null space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the null space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the null space of the src matrix.

    • getLeftNullSpace

      public static CMatrix getLeftNullSpace(CMatrix src)
      Computes an orthonormal basis of the left null space of a specified matrix.
      Parameters:
      src - Matrix to compute orthonormal basis of the left null space.
      Returns:
      A matrix containing as its columns, an orthonormal basis for the left null space of the src matrix.

    • hasEqualSpan

      public static boolean hasEqualSpan(Matrix src1, Matrix src2)
      Checks if two sets of vectors, stored as the columns of matrices, span the same space. That is, if each column of both matrices can be expressed as a linear combination of the columns of the other matrix.
      Parameters:
      src1 - Matrix containing as its columns the first set of vectors.
      src2 - Matrix containing as its columns the second set of vectors.
      Returns:
      True if the column vectors of src1 and src2 span the same space.

    • hasEqualSpan

      public static boolean hasEqualSpan(CMatrix src1, CMatrix src2)
      Checks if two sets of vectors, stored as the columns of matrices, span the same space. That is, if each column of both matrices can be expressed as a linear combination of the columns of the other matrix.
      Parameters:
      src1 - Matrix containing as its columns the first set of vectors.
      src2 - Matrix containing as its columns the second set of vectors.
      Returns:
      True if the column vectors of src1 and src2 span the same space.