Cálculo com matrizes

Ando fazendo uma revisão em álgebra linear e comecei a criar uma classe para fazer cálculos básicos com matrizes, para auxiliar em cálculos mais complexos posteriormente.

Abaixo segue a classe Matrix.

package br.lalgebra.math.matrix;

import br.lalgebra.math.errors.MatrixError;

public class Matrix
{

 /**
  * figure out the product between a factor and a matrix 
  * @param f
  * @param A
  * @return
  * @throws MatrixError
  */
 public static double[][] productNumber( double f, double A[][] ) throws MatrixError
 {
  double r[][] = null;
  
  if (A.length == 0) 
   throw new MatrixError("There is some empty matrix");

  // matrix A (mxn)  
  int m = A.length; int n = A[0].length;
  
  r = new double[m][n];
  
  for (int i = 0; i < m; i++) {
   for (int j = 0; j < n; j++)
    r[i][j] = f * A[i][j];
  }
  
  return r;
 }
 
 /**
  * figure out the matrix product
  * @param A
  * @param B
  * @return
  */
 public static double[][] product( double A[][], double B[][] ) throws MatrixError
 {
  
  double r[][] = null;
  
  if (A.length == 0 || B.length == 0) 
   throw new MatrixError("There is some empty matrix");
  
  // matrix A (mxn)  
  int m = A.length; int n = A[0].length;
  
  // matrix B (pxq)
  int p = B.length; int q = B[0].length;
  
  if (n != p) 
   throw new MatrixError("The number of columns of matrix A, must be the same of matrix B number of rows");
  
  double aux = 0.0;
  
  // defining the new array
  r = new double[m][q];
  
  // figuring out arrays product
  for (int i = 0; i < m; i++)
   for (int k = 0; k < q; k++) 
   {
    for (int j = 0; j < n; j++) 
     aux += A[i][j] * B[j][k];
    r[i][k] = aux;
    aux = 0;
   }
  
  return r;
 }
 
 public static String getString( double[][] x ) throws MatrixError
 {
  String result = "";

  if (x.length == 0) 
   throw new MatrixError("The matrix is empty");
  
  int m = x.length; int n = x[0].length;
  
  if (n == 0)
   throw new MatrixError("The matrix is empty");
  
  for (int i = 0; i < m; i++) {
   for (int j =0; j < n; j++)
    result += x[i][j] + "\t";
   result += "\n";
  }
  return result;
 }
}