Matrix represents a rectangular array of elements arranged in rows and columns (m X n)

To work with matrix, numpy provides a special object called matrix. It is a special 2D array that retains its 2D nature through operations.

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The syntax for creating a matrix is matrix_name = matrix(2D_array or string)

np. is needed depending on how numpy is imported.

>>> arr = np.reshape(np.arange(11,17), (2,3))
>>> arr
array([[11, 12, 13],
       [14, 15, 16]])
>>> np.matrix(arr)
matrix([[11, 12, 13],
        [14, 15, 16]])

>>> arr = np.reshape(np.arange(11,36), (5,5))
>>> arr
array([[11, 12, 13, 14, 15],
       [16, 17, 18, 19, 20],
       [21, 22, 23, 24, 25],
       [26, 27, 28, 29, 30],
       [31, 32, 33, 34, 35]])
>>> np.matrix(arr)
matrix([[11, 12, 13, 14, 15],
        [16, 17, 18, 19, 20],
        [21, 22, 23, 24, 25],
        [26, 27, 28, 29, 30],
        [31, 32, 33, 34, 35]])

Matrix can be directly typed inside the matrix also

>>> mat = np.matrix( [ [1,2,3,4],[4,3,2,1] ])
>>> mat
matrix([[1, 2, 3, 4],
        [4, 3, 2, 1]])

Or a string can be passed where elements of one array are separated by ; semicolon from elements of another array.

>>> mat = np.matrix( '1 2 3; 3 4 5; 6 7 8' )
>>> mat
matrix([[1, 2, 3],
        [3, 4, 5],
        [6, 7, 8]])

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Getting the diagonal elements of a matrix

Using the diagonal() function dia = diagonal(matrix)

>>> mat = np.matrix( "1 2; 3 4; 5 6" )
>>> mat
matrix([[1, 2],
        [3, 4],
        [5, 6]])

>>> dia = np.diagonal(mat)
>>> dia
matrix([1, 4])

Finding Maximum and Minimum Elements

max() min()

>>> mat = np.matrix( "1 2; 3 4; 5 6" )
>>> mat
matrix([[1, 2],
        [3, 4],
        [5, 6]])

>>> mat.min()
1

>>> mat.max()
6

Finding Sum and Average

sum() mean()

>>> mat.sum()
21

>>> mat.mean()
3.5

Product of Row or Column Elements

prod(0) returns matrix with products of elements in each column. prod(1) returns products in each row

>>> mat = np.matrix( np.arange(12).reshape(3,4) )
>>> mat
matrix([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]])

>>> col_prod = mat.prod(0)
>>> col_prod
matrix([[  0,  45, 120, 231]])

>>> row_prod = mat.prod(1)
>>> row_prod
matrix([[   0],
        [ 840],
        [7920]])

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Sorting Matrix

sort() function sorts the matrix elements into ascending order.

np.sort(matrix_name, axis=0/1) arr.sort(axis=0/1)

If axis = 0 it sorts the row elements. If axis = 1 it sorts the column elements.

Like Python’s built-in list type, NumPy arrays can be sorted in place with the sort method.

>>> mat = np.matrix( '5 2 1; 25 20 5; 15 4 8' )
>>> mat
matrix([[ 5,  2,  1],
        [25, 20,  5],
        [15,  4,  8]])

>>> mat.sort()
>>> mat
matrix([[ 1,  2,  5],
        [ 5, 20, 25],
        [ 4,  8, 15]])

>>> mat = np.matrix( '5 2 1; 25 20 5; 15 4 8' )
>>> mat.sort(axis=0)
>>> mat
matrix([[ 5,  2,  1],
        [15,  4,  5],
        [25, 20,  8]])

Works for arrays also:

>>> arr = np.array( [[ 5,  2,  1], [25, 20, 5 ], [15, 4, 8] ])
>>> arr
array([[ 5,  2,  1],
       [25, 20,  5],
       [15,  4,  8]])

>>> arr.sort()
>>> arr
array([[ 1,  2,  5],
       [ 5, 20, 25],
       [ 4,  8, 15]])

>>> arr.sort(axis=0)
>>> arr
array([[ 1,  2,  5],
       [ 4,  8, 15],
       [ 5, 20, 25]])

>>> arr = np.array( [[ 5,  2,  1], [25, 20, 5 ], [15, 4, 8] ])
>>> arr.sort(axis=0)
>>> arr
array([[ 5,  2,  1],
       [15,  4,  5],
       [25, 20,  8]])

The top-level method numpy.sort returns a sorted copy of an array (like the Python built-in function sorted) instead of modifying the array in place.

Passing the array or matrix as parameter to sort(arr) will not change the original and also returns the sorted array which can be assigned to a variable.

>>> mat = np.matrix([ [3,1,2],[5,2,8],[9,1,5] ])
>>> mat
matrix([[3, 1, 2],
        [5, 2, 8],
        [9, 1, 5]])

# Not specifying axis sorts the row elements
>>> row = np.sort(mat)
>>> row
matrix([[1, 2, 3],
        [2, 5, 8],
        [1, 5, 9]])

>>> row = np.sort(mat, axis=1)
>>> row
matrix([[1, 2, 3],
        [2, 5, 8],
        [1, 5, 9]])

# column sort with axis as 0
>>> col = np.sort(mat, axis=0)
>>> col
matrix([[3, 1, 2],
        [5, 1, 5],
        [9, 2, 8]])

---

Transpose of a matrix

Rows into columns and vice versa is called as transpose. A m X n matrix will become n X m.

Transpose can be done with transpose() and getT() methods in numpy.

>>> mat = np.matrix([ [3,1,2],[5,2,8],[9,1,5] ])
>>> mat
matrix([[3, 1, 2],
        [5, 2, 8],
        [9, 1, 5]])

>>> tra = mat.transpose()
>>> tra
matrix([[3, 5, 9],
        [1, 2, 1],
        [2, 8, 5]])

>>> mat = np.matrix([ [3,1,2],[5,2,8],[9,1,5],[10,15,1],[5,7,8] ])
>>> mat
matrix([[ 3,  1,  2],
        [ 5,  2,  8],
        [ 9,  1,  5],
        [10, 15,  1],
        [ 5,  7,  8]])

>>> tra = mat.transpose()
>>> tra
matrix([[ 3,  5,  9, 10,  5],
        [ 1,  2,  1, 15,  7],
        [ 2,  8,  5,  1,  8]])

Similarly for getT() also.

Matrix addition and multiplication

Math operators like +, -, *, / can be used to perform operations on 2 matrices.

>>> mat = np.matrix([ [3,1,2],[5,2,8],[9,1,5],[10,15,1],[5,7,8] ])
>>> mat1 = np.matrix(np.arange(15).reshape(5,3) )
>>> mat
matrix([[ 3,  1,  2],
        [ 5,  2,  8],
        [ 9,  1,  5],
        [10, 15,  1],
        [ 5,  7,  8]])

>>> mat1
matrix([[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8],
        [ 9, 10, 11],
        [12, 13, 14]])

>>> add = mat + mat1
>>> add
matrix([[ 3,  2,  4],
        [ 8,  6, 13],
        [15,  8, 13],
        [19, 25, 12],
        [17, 20, 22]])

>>> sub = mat - mat1
>>> sub
matrix([[  3,   0,   0],
        [  2,  -2,   3],
        [  3,  -6,  -3],
        [  1,   5, -10],
        [ -7,  -6,  -6]])

>>> sub = mat1 - mat
>>> sub
matrix([[-3,  0,  0],
        [-2,  2, -3],
        [-3,  6,  3],
        [-1, -5, 10],
        [ 7,  6,  6]])

>>> div = mat1 / mat
>>> div
matrix([[ 0.        ,  1.        ,  1.        ],
        [ 0.6       ,  2.        ,  0.625     ],
        [ 0.66666667,  7.        ,  1.6       ],
        [ 0.9       ,  0.66666667, 11.        ],
        [ 2.4       ,  1.85714286,  1.75      ]])

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Multiplication doesn't multiply the corresponding matrix elements, it needs the col of one to be equal to row of another. That is, if one is m x n, the other needs to be n x p. The resultant will be m x p.

Same kind of matrix format will not work unless it is a square matrix.

>>> prod = mat1 * mat
ValueError: shapes (5,3) and (5,3) not aligned: 3 (dim 1) != 5 (dim 0)

Transposing one of the matrices solves the problem if they are the same.

>>> mat1
matrix([[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8],
        [ 9, 10, 11],
        [12, 13, 14]])

# 5 x 3 matrix
# 3 x 5 matrix
>>> mat2 = mat.transpose()
>>> mat2
matrix([[ 3,  5,  9, 10,  5],
        [ 1,  2,  1, 15,  7],
        [ 2,  8,  5,  1,  8]])

# 5 x 5 matrix
>>> prod = mat1 * mat2
>>> prod
matrix([[  5,  18,  11,  17,  23],
        [ 23,  63,  56,  95,  83],
        [ 41, 108, 101, 173, 143],
        [ 59, 153, 146, 251, 203],
        [ 77, 198, 191, 329, 263]])

# Reversing the matrix
# 3 x 5 * 5 x 3 will be 3x3
>>> div = mat2 * mat1
>>> div
matrix([[219, 251, 283],
        [231, 257, 283],
        [159, 183, 207]])

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A program to accept two matrices and find their product

import sys
import numpy as np

r1, c1 = [int(a) for a in input("First matrix rows, cols: ").split()]

r2, c2 = [int(a) for a in input("Second matrix rows, cols: ").split()]

if c1 != r2:
    print("Multiplication not possible")
    sys.exit()

str1 = input("Enter first matrix elements: \n")
x = np.reshape(np.matrix(str1), (r1,c1))

str2 = input("Enter second matrix elements: \n")
y = np.reshape(np.matrix(str2), (r2,c2))

print("The product of the matrix: :")
z = x * y
z

Now, the arrays will be shown directly as outputs in the console!