Design of The MMath Class

Details

Encapsulating Matrices:

You must not create a class that encapsulates a matrix. Instead, you must use a double[][] to hold the elements.

Dimensionality Problems:

As you know, many operations involving matrices require that they be sized appropriately. When dimensionality problems arise the methods in this class must either return null or throw an IllegalArgumentException.

Side Effects:

The methods in this class must NOT change the parameters they are passed.

The cofactor() Method:

This class must include an implementation of the following method:

    /**
     * Calculate the cofactor of a square matrix
     * (i.e., the signed determinate of the mtraix with row
     * i and column j removed)
     *
     * @param a   The matrix (mxm)
     * @param i   The index of the row to exclude
     * @param j   The index of the col to exclude
     * @return    The cofactor
     */
    public static double cofactor(double[][] a, int i, int j)
  

The det() Method:

This class must include an implementation of the following method:

    /**
     * Calculate the determinant of a square matrix
     *
     * @param a   The matrix (mxm)
     * @return    The value of the determinant
     */
    public static double det(double[][] a)
  

The identity() Method:

This class must include an implementation of the following method:

    /**
     * Create an (nxn) identity matrix
     * 
     * @param n   The size of the (square) matrix
     * @return    The identity matrix
     */
    public double[][] identity(int n)
  

The minor() Method:

This class must include an implementation of the following method:

    /**
     * Create a particular minor from a square matrix
     *
     * @param a   The matrix (mxm)
     * @param i   The index of the row to exclude
     * @param j   The index of the col to exclude
     * @return    The minor (i.e., a with row i and column j excluded)
     */
    public static double minor(double[][] a, int i, int j)
  

The submatrix() Method:

This class must include an implementation of the following method:

    /**
     * Remove a row and column from a matrix
     *
     * @param a   The matrix (mxm)
     * @param i   The index of the row to exclude
     * @param j   The index of the col to exclude
     * @return    The submatrix (i.e., a with row i and column j excluded)
     */
    public static double[][] submatrix(double[][] a, int i, int j)
  

The sum() Method:

This class must include an implementation of the following method:

    /**
     * Add two matrices
     *
     * @param  a  One matrix
     * @param  b  The other matrix
     * @return    a + b
     */
    public static double[][] sum(double[][] a, double[][] b)
  

The times(double[], double[][]) Method:

This class must include an implementation of the following method:

    /**
     * Multiply a row vector and a matrix
     *
     * @param v   The row vector (1xn)
     * @param m   The matrix     (nxm)
     * @return    The resulting row vector (1xm)
     */
    public static double[] times(double[] v, double[][] m)
  

The times(double[][], double[][]) Method:

This class must include an implementation of the following method:

    /**
     * Multiply two matrices
     *
     * @param a   The first matrix (mxn)
     * @param b   The second matrix (nxs)
     * @return    The resulting matrix (mxs)
     */
    public static double[][] times(double[][] a, double[][] b) 
  

The transpose() Method:

This class must include an implementation of the following method:

    /**
     * Create the transpose of a matrix
     *
     * @param  a  The matrix
     * @return    a tranposed
     */
    public static double[][] transpose(double[][] a)