Day 6: Vector and Matrices¶
Today we will learn about two important data types of numpy library which is similar to vectors and matrices. Array and matrices stores data similar to lists but they suitable for mathematical operations like dot product and matrix multiplication.
1. Array¶
Here we will learn about array which is similar to vectors in mathematics.
1.1 Importing array¶
Similar to other python library we can import array as the following methods
import array
import array as arr
from array import *
Note
We will use only the second method in this course.
1.2 Creating Array elements¶
To make an array in python we use the following functions.
import array as arr
a = arr.array ('d' ,[1,2,3,4,5])
print(a)
This will create a array with variable a
contains five elements 1 to 5. Here d
denote the data type of float. For other datatype you can use the following table.
Code  C Type  Python Type  Min bytes 

b  signed char  int  1 
B  unsigned char  int  1 
u  Py_UNICODE  Unicode  2 
h  signed short  int  2 
H  unsigned short  int  2 
i  signed int  int  2 
I  unsigned int  int  2 
l  signed long  int  4 
L  unsigned long  int  4 
f  float  float  4 
d  double  float  8 
Tip
You can convert any list of number to an array simply using d
as in above code.
1.3 Accessing elements of array¶

Element: To access the an element of the array
a
, we use the following commandimport array as arr a = arr.array ('d' ,[1,2,3,4,5]) print(a[2]) # counting starts with 0 print(a[2]) # count from last
3 4

Slicing: Similar to the list and strings we can obtain a continuous part of an array
import array as arr a=arr.array('d', [6.8, 5.9, 9.8, 2.4, 3.3]) print(a[1:3]) # prints the part of array start with index 1 and end before 3
array('d', [5.9, 9.8])
1.4 Basic Array operations¶

len: Length of an array can be computed using
len
function as followsimport array as arr a = arr.array ('d' ,[1,2,3,4,5]) print(len(a)) # prints length of array a
5

Concatenation: We can join two array with
+
operation.import array as arr a = arr.array('d',[1.2, 5.8, 6.4]) b = arr.array('d',[1.3, 6]) c = a + b # array c will have elements of a and b print(c)
Array c = array('d', [1.2, 5.8, 6.4, 1.3, 6.0])
1.5 Method on array¶

append: Similar to the list the append is used to add a single element at the end of an array.
import array as arr a = arr.array ('d' ,[1,2,3,4,5]) a.append(23) # appends 23 at the end of array a print(a)
array('d', [1.0, 2.0, 3.0, 4.0, 5.0, 23.0])

extend: It is used when you want to add more than one element at the end of an array.
import array as arr a = arr.array ('d' ,[4,5]) a.extend([23, 4.15, 6.7]) # extend array a using list print(a) b = arr.array ('d' ,[23, 4.15, 6.7]) a.extend(b) # extend array a using another array b print(a)
array('d', [4.0, 5.0, 23.0, 4.15, 6.7]) array('d', [4.0, 5.0, 23.0, 4.15, 6.7, 23.0, 4.15, 6.7])

insert:  used when you want to add an element at a specific position in an array.
import array as arr a = arr.array ('d' ,[1.2,2,3.14,4,5]) a.insert(1, 2.73) # insert 2.73 at position 1 (count with 0) print(a)
array('d', [1.2, 2.73, 2.0, 3.14, 4.0, 5.0])

pop: It is used when you want to remove an element and return it. We can provide optional argument to remove an element with given index.
import array as arr a = arr.array('d', [4, 3, 5, 6.7, 3.5]) print(a.pop()) # remove the last element print(a.pop(1)) # remove index 1 element (count with 0) print(a)
3.5 3.0 array('d', [4.0, 5.0, 6.7])

remove: : It is used when you want to remove an element with a specific value without returning it.
import array as arr a = arr.array('d', [4, 3, 5, 6.7, 3.5]) print(a.remove(5)) # remove element 5, but produce no output print(a) # prints array a after removing element 5
None array('d', [4.0, 3.0, 6.7, 3.5])
1.6 Looping through an array¶
Similar to list and string we can use for loops or while loops to go through each elements of a list one by one.

for To iterates over the items of an array specified we can use for as follows
import array as arr a = arr.array('d', [6.8, 5.9, 9.8, 2.4, 3.3]) for i in a: # you can use each element on your desire print(i**2) # printing square of each element
46.239999999999995 34.81 96.04000000000002 5.76 10.889999999999999
2. Matrices in Python¶
Matrices in python can be achieved using one of the following ways
 Nested Lists
 Numpy Arrays
 Numpy Matrices
Now we will learn them one by one
2.1 Nested List¶
We can used nested list to store data similar to matrices.
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
print(matrix)
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Warning
Nested list doesn't work similar to matrices in mathematics. They are simply table and operations are limited by list functions.
2.2 Numpy Arrays¶
Similar to nested list, we can use array inside array to store data in matrices.
import numpy as np
a = np.array([[1.2, 2.1],[3.6, 4.3]])
print(a)
[[1.2 2.1]
[3.6 4.3]]
2.2.1 Operation on matrices¶

Addition: We use
+
to achieve addition of similar size matrices.import numpy as np a = np.array([[1, 2], [3, 4]]) b = np.array([[10, 20], [30, 40]]) print(a + b)
[[11 22] [33 44]]

Matrix multiplication: We use
*
to achieve addition of similar size matrices.import numpy as np a = np.array([[1, 2], [3, 4]]) b = np.array([[10, 20], [30, 40]]) print(a * b)
[[ 10 40] [ 90 160]]

Transpose: We can transpose a matrix using the
transpose
function ofnumpy
library.import numpy as np a = np.array([[1,2,3],[4,5,6]]) print(a) print(np.transpose(a))
[[1 2 3] [4 5 6]] [[1 4] [2 5] [3 6]]
2.3 Numpy Matrices¶
Numpy matrix is a class in nunpy library to handle matrices and mathematical operations related to them.
2.3.1 creating a matrix from a string¶
The main advantage of this class is that it has flexible method of creating matrices and slicing them.
import numpy as np
a = np.matrix("1, 2; 3, 4")
b = np.matrix([[10, 20],[30, 40]])
print(a)
print(b)
[[1 2]
[3 4]]
[[10 20]
[30 40]]
2.3.2 Operations on Numpy Matrices¶
The operation on numpy matrices are similar to the matrices we make using numpy arrays.