{"id":3078,"date":"2020-02-04T12:14:36","date_gmt":"2020-02-04T12:14:36","guid":{"rendered":"https:\/\/www.askpython.com\/?p=3078"},"modified":"2023-02-16T19:57:17","modified_gmt":"2023-02-16T19:57:17","slug":"python-matrix-tutorial","status":"publish","type":"post","link":"https:\/\/www.askpython.com\/python\/python-matrix-tutorial","title":{"rendered":"Python Matrix Tutorial"},"content":{"rendered":"\n

We can implement a Python Matrix in the form of a 2-d List<\/strong> or a 2-d Array<\/strong>. To perform operations on Python Matrix, we need to import Python NumPy Module.<\/strong><\/p>\n\n\n\n

Python Matrix is essential in the field of statistics, data processing, image processing, etc.<\/p>\n\n\n\n

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Creation of a Python Matrix<\/h2>\n\n\n\n

Python Matrix can be created using one of the following techniques:<\/p>\n\n\n\n

  • By using Lists<\/strong><\/li>
  • By using arange() method<\/strong><\/li>
  • By using matrix() method<\/strong><\/li><\/ul>\n\n\n\n

    1. Creation of matrix using Lists<\/h3>\n\n\n\n

    The numpy.array()<\/code> function can be used to create an array using lists as input to it<\/strong>.<\/p>\n\n\n\n

    Example:<\/strong><\/p>\n\n\n

    \nimport numpy\ninput_arr = numpy.array([[ 10, 20, 30],[ 40, 50, 60]])\nprint(input_arr)\n<\/pre><\/div>\n\n\n
    Output:<\/strong><\/p>\n\n\n
    \n[[10 20 30]\n [40 50 60]]\n<\/pre><\/div>\n\n\n
    As seen above, the output represents a 2-D matrix with the given set of inputs in the form of list.<\/p>\n\n\n\n
    2. Creation of matrix using ‘numpy.arange()’ function<\/h3>\n\n\n\n
    The numpy.arange()<\/code> function along with the list inputs can be used to create a matrix in Python.<\/p>\n\n\n\n
    Example:<\/strong><\/p>\n\n\n
    \nimport numpy\n\nprint(numpy.array([numpy.arange(10,15), numpy.arange(15,20)]))\n \n<\/pre><\/div>\n\n\n
    Output:<\/strong><\/p>\n\n\n
    \n[[10 11 12 13 14]\n [15 16 17 18 19]]\n<\/pre><\/div>\n\n\n
    3. Creation of Matrix using ‘numpy.matrix() function’<\/h3>\n\n\n\n
    The numpy.matrix()<\/code> function enables us to create a matrix in Python.<\/p>\n\n\n\n
    Syntax:<\/strong><\/p>\n\n\n
    \nnumpy.matrix(input,dtype)\n<\/pre><\/div>\n\n\n
    • input: The elements input to form a matrix.<\/strong><\/li>
    • dtype: The data type of the corresponding output.<\/strong><\/li><\/ul>\n\n\n\n
      Example:<\/strong><\/p>\n\n\n
      \nimport numpy as p\n\n\nmatA = p.matrix([[10, 20], [30, 40]])  \nprint('MatrixA:\\n', matA)\n\n\n\nmatB = p.matrix('[10,20;30,40]', dtype=p.int32)  # Setting the data-type to int\nprint('\\nMatrixB:\\n', matB)\n\n<\/pre><\/div>\n\n\n
      Output:<\/strong><\/p>\n\n\n
      \nMatrixA:\n [[10 20]\n [30 40]]\n\nMatrixB:\n [[10 20]\n [30 40]]\n<\/pre><\/div>\n\n\n
      \n\n\n\n
      Addition of Matrix in Python<\/h2>\n\n\n\n
      The addition operation on Matrices can be performed in the following ways:<\/p>\n\n\n\n
      • Traditional method<\/strong><\/li>
      • By using ‘+’ operator<\/strong><\/li><\/ul>\n\n\n\n
        1. Traditional method<\/h3>\n\n\n\n
        In this traditional method, we basically take the input from the user and then perform the addition operation using the for loops<\/strong> (to traverse through the elements of the matrix) and ‘+’ operator<\/strong>. <\/p>\n\n\n\n
        Example:<\/strong><\/p>\n\n\n
        \nimport numpy as p\n\n\nar1 = p.matrix([[11, 22], [33, 44]])  \nar2 = p.matrix([[55, 66], [77, 88]])  \nres = p.matrix(p.zeros((2,2)))  \nprint('Matrix ar1 :\\n', ar1)\nprint('\\nMatrix ar2 :\\n', ar2)\n\n# traditional code\nfor x in range(ar1.shape[1]):\n    for y in range(ar2.shape[0]):\n        res[x, y] = ar1[x, y] + ar2[x, y]\n\nprint('\\nResult :\\n', res)\n\n\n<\/pre><\/div>\n\n\n
        Note<\/strong>:Matrix.shape<\/code> returns the dimensions of a particular matrix.<\/p>\n\n\n\n
        Output:<\/strong><\/p>\n\n\n
        \nMatrix ar1 :\n [[11 22]\n [33 44]]\n\nMatrix ar2 :\n [[55 66]\n [77 88]]\n\nResult :\n [[  66.   88.]\n [ 110.  132.]]\n\n<\/pre><\/div>\n\n\n
        2. Using ‘+’ operator<\/h3>\n\n\n\n
        This method provides better efficiency to the code as it reduces the LOC (lines of code) and thus, optimizes the code.<\/p>\n\n\n\n
        Example:<\/strong><\/p>\n\n\n
        \nimport numpy as p\n\n\nar1 = p.matrix([[11, 22], [33, 44]])  \nar2 = p.matrix([[55, 66], [77, 88]])  \nres = p.matrix(p.zeros((2,2)))  \nprint('Matrix ar1 :\\n', ar1)\nprint('\\nMatrix ar2 :\\n', ar2)\n\nres = ar1 + ar2 # using '+' operator\n\nprint('\\nResult :\\n', res)\n\n\n<\/pre><\/div>\n\n\n
        Output:<\/strong><\/p>\n\n\n
        \nMatrix ar1 :\n [[11 22]\n [33 44]]\n\nMatrix ar2 :\n [[55 66]\n [77 88]]\n\nResult :\n [[ 66  88]\n [110 132]]\n<\/pre><\/div>\n\n\n
        \n\n\n\n
        Matrix Multiplication in Python<\/h2>\n\n\n\n
        Matrix Multiplication in Python can be provided using the following ways:<\/p>\n\n\n\n
        • Scalar Product<\/strong><\/li>
        • Matrix Product<\/strong><\/li><\/ul>\n\n\n\n
          Scalar Product<\/h3>\n\n\n\n
          In the scalar product, a scalar\/constant value<\/strong> is multiplied by each element of the matrix.<\/p>\n\n\n\n
          The ‘*’ operator <\/strong>is used to multiply the scalar value with the input matrix elements.<\/p>\n\n\n\n
          Example:<\/strong><\/p>\n\n\n
          \nimport numpy as p\n\nmatA = p.matrix([[11, 22], [33, 44]])  \n\nprint("Matrix A:\\n", matA)\nprint("Scalar Product of Matrix A:\\n", matA * 10)\n\n\n<\/pre><\/div>\n\n\n
          Output:<\/strong><\/p>\n\n\n
          \nMatrix A:\n [[11 22]\n [33 44]]\nScalar Product of Matrix A:\n [[110 220]\n [330 440]]\n<\/pre><\/div>\n\n\n
          Matrix Product<\/h3>\n\n\n\n
          As mentioned above, we can use the ‘*’ operator only for Scalar multiplication<\/strong>. In order to go ahead with Matrix multiplication, we need to make use of the numpy.dot()<\/code> function.<\/p>\n\n\n\n
          The numpy.dot()<\/code> function takes NumPy arrays as parameter<\/strong> values and performs multiplication according to the basic rules of Matrix Multiplication.<\/p>\n\n\n\n
          Example:<\/strong><\/p>\n\n\n
          \nimport numpy as p\n\nmatA = p.matrix([[11, 22], [33, 44]])  \nmatB = p.matrix([[2,2], [2,2]])\n\nprint("Matrix A:\\n", matA)\nprint("Matrix B:\\n", matB)\nprint("Dot Product of Matrix A and Matrix B:\\n", p.dot(matA, matB))\n\n<\/pre><\/div>\n\n\n
          Output:<\/strong><\/p>\n\n\n
          \nMatrix A:\n [[11 22]\n [33 44]]\nMatrix B:\n [[2 2]\n [2 2]]\nDot Product of Matrix A and Matrix B:\n [[ 66  66]\n [154 154]]\n<\/pre><\/div>\n\n\n
          \n\n\n\n
          Subtraction of Python Matrix<\/h2>\n\n\n\n
          The ‘-‘ operator<\/strong> is used to perform Subtraction on Python Matrix.<\/p>\n\n\n\n
          Example:<\/strong><\/p>\n\n\n
          \nimport numpy as p\n\nmatA = p.matrix([[11, 22], [33, 44]])  \nmatB = p.matrix([[2,2], [2,2]])\n\nprint("Matrix A:\\n", matA)\nprint("Matrix B:\\n", matB)\nprint("Subtraction of Matrix A and Matrix B:\\n",(matA - matB))\n \n<\/pre><\/div>\n\n\n
          Output:<\/strong><\/p>\n\n\n
          \nMatrix A:\n [[11 22]\n [33 44]]\nMatrix B:\n [[2 2]\n [2 2]]\nSubtraction of Matrix A and Matrix B:\n [[ 9 20]\n [31 42]]\n<\/pre><\/div>\n\n\n
          \n\n\n\n
          Division of Python Matrix<\/h2>\n\n\n\n
          Scalar Division<\/strong> can be performed on the elements of the Matrix in Python using the ‘\/’ operator<\/strong>.<\/p>\n\n\n\n
          The ‘\/’ operator divides each element of the Matrix with a scalar\/constant value.<\/p>\n\n\n\n
          Example<\/strong>:<\/p>\n\n\n
          \nimport numpy as p\n\n\nmatB = p.matrix([[2,2], [2,2]])\n\n\nprint("Matrix B:\\n", matB)\nprint("Matrix B after Scalar Division operation:\\n",(matB\/2))\n \n<\/pre><\/div>\n\n\n
          Output:<\/strong><\/p>\n\n\n
          \nMatrix B:\n [[2 2]\n [2 2]]\nMatrix B after Scalar Division operation:\n [[ 1.  1.]\n [ 1.  1.]]\n<\/pre><\/div>\n\n\n
          \n\n\n\n
          Transpose of a Python Matrix<\/h2>\n\n\n\n
          Transpose of a matrix basically involves the flipping of matrix over the corresponding diagonals<\/strong> i.e. it exchanges the rows and the columns of the input matrix. The rows become the columns and vice-versa.<\/p>\n\n\n\n
          For example: Let’s consider a matrix A with dimensions 3×2 i.e 3 rows and 2 columns. After performing transpose operation, the dimensions of the matrix A would be 2×3 i.e 2 rows and 3 columns.<\/p>\n\n\n\n
          Matrix.T<\/code> basically performs the transpose of the input matrix and produces a new matrix<\/strong> as a result of the transpose operation.<\/p>\n\n\n\n
          Example:<\/strong><\/p>\n\n\n
          \nimport numpy\n \nmatA = numpy.array([numpy.arange(10,15), numpy.arange(15,20)])\nprint("Original Matrix A:\\n")\nprint(matA)\nprint('\\nDimensions of the original MatrixA: ',matA.shape)\nprint("\\nTranspose of Matrix A:\\n ")\nres = matA.T\nprint(res)\nprint('\\nDimensions of the Matrix A after performing the Transpose Operation:  ',res.shape)\n<\/pre><\/div>\n\n\n
          Output:<\/strong><\/p>\n\n\n
          \nOriginal Matrix A:\n\n[[10 11 12 13 14]\n [15 16 17 18 19]]\n\nDimensions of the original MatrixA: (2, 5)\n\nTranspose of Matrix A:\n \n[[10 15]\n [11 16]\n [12 17]\n [13 18]\n [14 19]]\n\nDimensions of the Matrix A after performing the Transpose Operation: (5, 2)\n<\/pre><\/div>\n\n\n
          In the above snippet of code, I have created a matrix of dimensions 2×5 i.e. 2 rows and 5 columns.<\/p>\n\n\n\n
          After performing the transpose operation, the dimensions of the resultant matrix are 5×2 i.e. 5 rows and 2 columns.<\/p>\n\n\n\n
          \n\n\n\n
          Exponent of a Python Matrix<\/h2>\n\n\n\n
          The exponent on a Matrix is calculated element-wise<\/strong> i.e. exponent of every element is calculated by raising the element to the power of an input scalar\/constant value.<\/p>\n\n\n\n
          Example:<\/strong><\/p>\n\n\n
          \nimport numpy\n \nmatA = numpy.array([numpy.arange(0,2), numpy.arange(2,4)])\nprint("Original Matrix A:\\n")\nprint(matA)\nprint("Exponent of the input matrix:\\n")\nprint(matA ** 2) # finding the exponent of every element of the matrix\n\n<\/pre><\/div>\n\n\n
          Output:<\/strong><\/p>\n\n\n
          \nOriginal Matrix A:\n\n[[0 1]\n [2 3]]\n\nExponent of the input matrix:\n\n[[0 1]\n [4 9]]\n<\/pre><\/div>\n\n\n
          In the above code snippet, we have found out the exponent of every element of the input matrix by raising it to the power of 2.<\/p>\n\n\n\n
          \n\n\n\n
          Matrix Multiplication Operation using NumPy Methods<\/h2>\n\n\n\n
          The following techniques can be used to perform NumPy Matrix multiplication:<\/p>\n\n\n\n