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Scalar arithmetic operation on Matrix

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An Arithmetic operation (addition or subtraction or multiplication or division) is carried out between a matrix and a scalar constant. In which each element of the matrix individually undergoes arithmetic operation by the consultant.

Assume that, A is matrix and c is a scalar constant and an arithmetic operation addition i.e (A + c) The following figure shows how to add scalar constant over a matrix.

scalar addition over a matrix

The results of a scalar constant addition over a matrix is each elements of the matrix added by the constant c.


Matrix scalar addition

Each elements of the matrix is added by the constant c. The example shown below a 3x3 matrix is added by a scalar constant 2


Matrix scalar subtraction

Each elements of the matrix is subtracted by the constant c. The example shown below a 3x3 matrix is subtracted by a scalar constant 4


Matrix scalar multiplication

Each elements of the matrix is multiplied by the constant c. The example shown below a 3x3 matrix is multiplied by a scalar constant 2


Matrix scalar division

Each elements of the matrix is divided by the constant c. The example shown below a 3x3 matrix is divided by a scalar constant 2



Scalar arithmetic on matrix - Java programming code

The Java program has five static member functions (add, subtract,multiply,divide and power) to carry out arithmetic operation over matrix by a scalar constant. 

 
public class Scalar {

 public static  Matrix add(Matrix mat,double scalar) 
  {
       Matrix mat2 =new Matrix(mat.getNrow(),mat.getNcol());
       for(int r=0;r<mat.getNrow();r++) {       
            for(int c=0;c<mat.getNcol();c++)              
                 mat2.setElement(r,c, mat.getElement(r,c)+scalar);      
           }  
        return mat2;
   }
   
  public static Matrix subtract(Matrix mat,double scalar) 
  {
       Matrix mat2 =new Matrix(mat.getNrow(),mat.getNcol());
       for(int r=0;r<mat.getNrow();r++) {       
           for(int c=0;c<mat.getNcol();c++)
                 mat2.setElement(r,c, mat.getElement(r,c)-scalar);     
          }
       return mat2;
   }
   
 public static Matrix multiply(Matrix mat,double scalar) 
   { 
        Matrix mat2 =new Matrix(mat.getNrow(),mat.getNcol());
        for(int r=0;r<mat.getNrow();r++) 
          {       
            for(int c=0;c<mat.getNcol();c++)
                mat2.setElement(r,c, mat.getElement(r,c)*scalar);
          }
         return mat2;
   }

  public static Matrix power(Matrix mat,double scalar) 
   {   
       Matrix mat2 =new Matrix(mat.getNrow(),mat.getNcol());
       for(int r=0;r<mat.getNrow();r++) 
          {       
              for(int c=0;c<mat.getNcol();c++)
                 mat2.setElement(r,c, Math.pow(mat.getElement(r,c),scalar));    
          }
       return mat2;
   }
   
  public static Matrix divide(Matrix mat,double scalar) 
   {   
       Matrix mat2 =new Matrix(mat.getNrow(),mat.getNcol());
       for(int r=0;r<mat.getNrow();r++) 
         {       
           for(int c=0;c<mat.getNcol();c++)
             mat2.setElement(r,c, mat.getElement(r,c)/scalar);    
         }
    return mat2;
   }
   
 
 public static void main(String[] args) {
  
     double vals[][]={{3,1,2},{2,-1,1},{1,3,-1}};     
     Matrix A =new Matrix(vals);
     System.out.println("Matrix A");
     System.out.println(A.toString());
 
     System.out.println("Matrix A+5");          
      Matrix B=Scalar.add(A, 5);
     System.out.println(B.toString());
     
     System.out.println("Matrix A-3");          
      Matrix C=Scalar.multiply(A, 3);
     System.out.println(C.toString());

     System.out.println("Matrix A.*2");          
      Matrix D=Scalar.multiply(A, 2);
     System.out.println(D.toString());
          
     System.out.println("Matrix A./0.5");          
      Matrix E=Scalar.divide(A, 0.5);
     System.out.println(E.toString());
     
     System.out.println("Matrix A.^2");          
      Matrix F=Scalar.power(A, 2);
     System.out.println(F.toString());          
 }

}

Scalar arithmetic on matrix - Java programming Output


 Matrix A
3.0  1.0  2.0  
2.0  -1.0  1.0  
1.0  3.0  -1.0  

Matrix A+5
8.0  6.0  7.0  
7.0  4.0  6.0  
6.0  8.0  4.0  

Matrix A-3
0.0  -2.0  -1.0  
-1.0  -4.0  -2.0  
-2.0  0.0  -4.0  

Matrix A.*2
6.0  2.0  4.0  
4.0  -2.0  2.0  
2.0  6.0  -2.0  

Matrix A./0.5
6.0  2.0  4.0  
4.0  -2.0  2.0  
2.0  6.0  -2.0  

Matrix A.^2
9.0  1.0  4.0  
4.0  1.0  1.0  
1.0  9.0  1.0

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