How to make a matrix using arrays?

MatricesMatrices are the plural form of a matrix have various applications in computer science and mathematics, enabling quick approximations to complex calculations.

Programming languages use arrays, specifically two-dimensional arrays, to create a matrix. A two-dimensional array is an array that contains references (the "rows" of the matrix) to other arrays (the "columns" of the matrix), as illustrated in the diagram below.

Producing a two-dimensional array (Array 5) from multiple one-dimensional arrays (Array 1–4)

The elements of the two-dimensional array above (Array 5) aren't integers, rather they're references to the one-dimensional arrays, Array 1–4.

Creating a matrix

The code snippets below goes over how to program a two-dimensional array similar to the one in the illustration above (Array 5).

int array1[4] = {3, 5, 1, 6};
int array2[4] = {1, 7, 2, 9};
int array3[4] = {9, 3, 7, 2};
int array4[4] = {6, 2, 4, 6};
int* exampleMatrix[4] = {array1, array2, array3, array4};

Code explanation

C++

  • Line 1-4: We declare all the rows of our matrix.

  • Line 6: We assign an array containing references to above four arrays (rows of the matrix) to pointer variable exampleMatrix.

Python

  • Line 1-4: We declare all the rows of our matrix.

  • Line 6: We create matrix exampleMatrix containing references to above four arrays (rows of the matrix).

Printing a matrix

In order to print the matrix (two-dimensional array), we make use of nested for loops, as depicted in the code snippets below.

Note: The dimensions of the matrix must be known before printing it.

for (int i = 0; i < 4; i++){
  for (int j = 0; j < 4; j++){
    cout << exampleMatrix[i][j] << " ";
  }
  cout << endl;
}

Code explanation

C++

  • Line 1-6: We print the two dimensional matrix using two nested for loops.

Python

  • Line 1-6: We print the two dimensional matrix using Python's print function.

Indexing a two-dimensional array

Two-dimensional arrays are most often indexed using the bracket notation, as can be seen below:

Using bracket notation to index a two-dimensional array

The bracket notation above will result in indexing the element that is present at the ith row and jth column of our matrix, exampleMatrix.

In order to assign a value to this element, we make use of the assignment operator. Below, the value of 8 is assigned to the element in the 2nd row and 3rd column of exampleMatrix.

exampleMatrix[2][3] = 8;
// Printing the matrix
for (int i = 0; i < 4; i++){
  for (int j = 0; j < 4; j++){
    cout << exampleMatrix[i][j] << " ";
  }
  cout << endl;
}

Code explanation

C++

  • Line 1: We assign the value 8 to the element of second row and third column in exampleMatrix.

  • Line 4-9: We print the complete matrix using nested for loops.

Python

  • Line 1: We assign the value 8 to the element of second row and third column in exampleMatrix.

  • Line 5: We print the complete matrix using print function.

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