Tutorial Playlist
200 Lessons1. Introduction to Python
2. Features of Python
3. How to install python in windows
4. How to Install Python on macOS
5. Install Python on Linux
6. Hello World Program in Python
7. Python Variables
8. Global Variable in Python
9. Python Keywords and Identifiers
10. Assert Keyword in Python
11. Comments in Python
12. Escape Sequence in Python
13. Print In Python
14. Python-if-else-statement
15. Python for Loop
16. Nested for loop in Python
17. While Loop in Python
18. Python’s do-while Loop
19. Break in Python
20. Break Pass and Continue Statement in Python
21. Python Try Except
22. Data Types in Python
23. Float in Python
24. String Methods Python
25. List in Python
26. List Methods in Python
27. Tuples in Python
28. Dictionary in Python
29. Set in Python
30. Operators in Python
31. Boolean Operators in Python
32. Arithmetic Operators in Python
33. Assignment Operator in Python
34. Bitwise operators in Python
35. Identity Operator in Python
36. Operator Precedence in Python
37. Functions in Python
38. Lambda and Anonymous Function in Python
39. Range Function in Python
40. len() Function in Python
41. How to Use Lambda Functions in Python?
42. Random Function in Python
43. Python __init__() Function
44. String Split function in Python
45. Round function in Python
46. Find Function in Python
47. How to Call a Function in Python?
48. Python Functions Scope
49. Method Overloading in Python
50. Method Overriding in Python
51. Static Method in Python
52. Python List Index Method
53. Python Modules
54. Math Module in Python
55. Module and Package in Python
56. OS module in Python
57. Python Packages
58. OOPs Concepts in Python
59. Class in Python
60. Abstract Class in Python
61. Object in Python
62. Constructor in Python
63. Inheritance in Python
64. Multiple Inheritance in Python
65. Encapsulation in Python
66. Data Abstraction in Python
67. Opening and closing files in Python
68. How to open JSON file in Python
69. Read CSV Files in Python
70. How to Read a File in Python
71. How to Open a File in Python?
72. Python Write to File
73. JSON Python
74. Python JSON – How to Convert a String to JSON
75. Python JSON Encoding and Decoding
76. Exception Handling in Python
77. Recursion in Python
78. Python Decorators
79. Python Threading
80. Multithreading in Python
81. Multiprocеssing in Python
82. Python Regular Expressions
83. Enumerate() in Python
84. Map in Python
85. Filter in Python
86. Eval in Python
87. Difference Between List, Tuple, Set, and Dictionary in Python
88. List to String in Python
89. Linked List in Python
90. Length of list in Python
91. Reverse a List in Python
92. Python List remove() Method
93. How to Add Elements in a List in Python
94. How to Reverse a List in Python?
95. Difference Between List and Tuple in Python
96. List Slicing in Python
97. Sort in Python
98. Merge Sort in Python
99. Selection Sort in Python
100. Sort Array in Python
101. Sort Dictionary by Value in Python
102. Datetime Python
103. Random Number in Python
104. 2D Array in Python
105. Abs in Python
106. Advantages of Python
107. Anagram Program in Python
108. Append in Python
109. Applications of Python
110. Armstrong Number in Python
111. Assert in Python
112. Binary Search in Python
113. Binary to Decimal in Python
114. Bool in Python
115. Calculator Program in Python
116. chr in Python
117. Control Flow Statements in Python
118. Convert String to Datetime Python
119. Count in python
120. Counter in Python
121. Data Visualization in Python
122. Datetime in Python
123. Extend in Python
124. F-string in Python
125. Fibonacci Series in Python
126. Format in Python
127. GCD of Two Numbers in Python
128. How to Become a Python Developer
129. How to Run Python Program
130. In Which Year Was the Python Language Developed?
131. Indentation in Python
132. Index in Python
133. Interface in Python
134. Is Python Case Sensitive?
135. Isalpha in Python
136. Isinstance() in Python
137. Iterator in Python
138. Join in Python
139. Leap Year Program in Python
140. Lexicographical Order in Python
141. Literals in Python
142. Matplotlib
143. Matrix Multiplication in Python
Now Reading
144. Memory Management in Python
145. Modulus in Python
146. Mutable and Immutable in Python
147. Namespace and Scope in Python
148. OpenCV Python
149. Operator Overloading in Python
150. ord in Python
151. Palindrome in Python
152. Pass in Python
153. Pattern Program in Python
154. Perfect Number in Python
155. Permutation and Combination in Python
156. Prime Number Program in Python
157. Python Arrays
158. Python Automation Projects Ideas
159. Python Frameworks
160. Python Graphical User Interface GUI
161. Python IDE
162. Python input and output
163. Python Installation on Windows
164. Python Object-Oriented Programming
165. Python PIP
166. Python Seaborn
167. Python Slicing
168. type() function in Python
169. Queue in Python
170. Replace in Python
171. Reverse a Number in Python
172. Reverse a string in Python
173. Reverse String in Python
174. Stack in Python
175. scikit-learn
176. Selenium with Python
177. Self in Python
178. Sleep in Python
179. Speech Recognition in Python
180. Split in Python
181. Square Root in Python
182. String Comparison in Python
183. String Formatting in Python
184. String Slicing in Python
185. Strip in Python
186. Subprocess in Python
187. Substring in Python
188. Sum of Digits of a Number in Python
189. Sum of n Natural Numbers in Python
190. Sum of Prime Numbers in Python
191. Switch Case in Python
192. Python Program to Transpose a Matrix
193. Type Casting in Python
194. What are Lists in Python?
195. Ways to Define a Block of Code
196. What is Pygame
197. Why Python is Interpreted Language?
198. XOR in Python
199. Yield in Python
200. Zip in Python
Matrix multiplication is a fundamental operation in linear algebra, used in various fields such as physics, engineering, computer graphics, and machine learning. In Python, you can perform matrix multiplication efficiently using different methods and libraries. This guide will explore matrix multiplication in Python, including various techniques and tools for performing this operation.
Matrices serve as fundamental mathematical constructs that find widespread applications across diverse fields such as mathematics, physics, engineering, computer science, and more. In specific contexts, such as deep learning and various statistical tasks, matrices and their operations, including multiplication and matrix addition in Python, play a crucial role in generating predictions based on input data.
Matrix multiplication, a concept first elucidated by Jacques Binet in 1812, constitutes a binary operation that involves two matrices, each possessing dimensions denoted as (a×b) and (b×c). The outcome of this operation is yet another matrix, referred to as the product matrix, with dimensions (a×c). While the process of matrix multiplication may appear intricate initially, it essentially adheres to a straightforward method.
Calculating the product of two matrices, A and B, denoted as AB, involves the following sequential steps:
1. Ensure that the first matrix, A, possesses an equal number of rows as the second matrix, B, has columns. In simpler terms, their dimensions must align in the format of (a×b) and (b×c) respectively. Without this alignment, multiplication between the matrices is not feasible.
2. Initialize an empty matrix, denoted as C, which will ultimately store the product.
3. Iterate through all combinations of indices (i, j), where 0 <= i < a and 0 <= j < c:
Extract the ith row from matrix A and the jth column from matrix B. Proceed to multiply corresponding elements at the same index, effectively forming a series of products.
Sum up the products obtained in the previous step.
Place this sum in the cell located at the intersection of row i and column j within the product matrix C.
4. As a final validation step, ensure that the resultant product matrix adheres to the dimensions (a×c). This step confirms the correctness of the matrix multiplication process.
Matrix multiplication in Java is a binary operation that takes a pair of matrices and produces another matrix. It combines elements from the rows of the first matrix with the columns of the second.
Matrix multiplication is a fundamental mathematical operation that results in the creation of a brand-new matrix by multiplying two pre-existing matrices. This intricate process involves executing precise arithmetic operations on elements found in corresponding positions within the original matrices. Each element in the resulting matrix is determined through these operations, making matrix multiplication a powerful mathematical tool.
A crucial aspect to bear in mind is that matrix multiplication adheres to specific rules. It is a valid operation only when the number of columns in the first matrix aligns perfectly with the number of rows in the second matrix. This alignment is paramount for the multiplication to yield meaningful results, underscoring the importance of dimension compatibility.
In the world of Python, matrices are frequently represented using nested lists. Within this representation, each element in the outer list corresponds directly to a row within the matrix. For instance, envision a 3×2 matrix denoted as X = [[1, 2], [4, 5], [3, 6]]. In this arrangement, each sub-list signifies a row, and the values inside these sub-lists denote the elements in their respective columns.
Accessing specific elements within a matrix in Python involves utilizing indices. For example, should you wish to retrieve the first row of the matrix X, you can employ the notation X[0]. Similarly, if you aim to pinpoint a particular element, X[0][0] provides the means to reference the element at the intersection of the first row and the first column. This indexing system facilitates precise data extraction within matrices, enabling you to work with the information as needed.
Matrix multiplication in Python involves taking the dot product of rows from the first matrix with columns from the second. This operation requires the number of columns in the first matrix to be equal to the number of rows in the second for it to be valid.
In this method for matrix multiplication in Python, we employ a nested for loop to multiply two matrices and store the resulting values in a third matrix.
While this approach is straightforward, it becomes computationally intensive as the matrix size increases. For larger matrix operations, we recommend using NumPy because it can be significantly faster (in the order of 1000 times) than the code described above.
# multiply two matrices using nested for loops
# 3x3 matrix
A = [[1,2,3],
[4,5,6],
[7,8,9]]
# 3x4 matrix
B = [[1,2,3,4],
[5,6,7,8],
[2,4,6,8]]
# result is 3x4
result = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0]]
# iterate across Matrix A rows
for i in range(len(A)):
# iterate through Matrix B columns
for j in range(len(B[0])):
# iterate through rows of Matrix B
for k in range(len(B)):
result[i][j] += A[i][k] * B[k][j] # Corrected line
print('Multiplied Matrix:')
for r in result:
print(r)
Output:
Multiplied Matrix:
[18, 24, 30, 36]
[45, 60, 75, 90]
[72, 96, 120, 144]
Here's an explanation of the program:
First, we define and initialize a collection of variables that will be utilized throughout the program.
The initial matrix will be found in A.
The second matrix will be stored in B.
The values of the generated matrices will be stored in the result.
Iteration is accomplished with i, j, and k.
In our program, we utilize nested for loops to traverse through each row and column. The matrix inverse Python multiplication is done by multiplying the corresponding elements of the first matrix (A) by the associated elements of the second matrix (B) throughout each iteration.
The outcomes yielded by this code are consistent with those of the prior example. In this matrix multiplication list comprehension Python, we leverage the power of nested list comprehensions to compute the product of two given matrices.
This method includes iteratively going over each matrix member using nested list comprehensions, which results in less Python code.
To fully grasp and utilize this method, a solid comprehension of the built-in `zip()` function and the ability to unpack argument lists using the `*` operators are crucial.
# Program to multiply two matrices using list comprehension
# 3x3 matrix
A = [[1,2,3],
[4,5,6],
[7,8,9]]
# 3x4 matrix
B = [[1,2,3,4],
[5,6,7,8],
[2,4,6,8]]
# result is 3x4
result = ''[[sum(a*b for a,b in zip(A_row, B col)) for B_col in zip(*B)] for A_row in A]"
print('Multiplied Matrix:')
for r in result:
print(r)
Output
Multiplied Matrix:
[17, 26, 35, 44]
[41, 62, 83, 104]
[65, 98, 131, 164]
An essential Python concept to grasp before delving into the next approach for implementing our matrix multiplication program is vectorization.
Vectorization involves the execution of loops without the need to explicitly create them. It harnesses the power of NumPy methods, leveraging pre-compiled and optimized C-code, as well as potential parallel processing capabilities (if supported by the hardware) to perform rapid and efficient looping operations. Extensive benchmarking on substantial datasets has demonstrated that vectorization can yield a significant boost in performance compared to conventional Python loops. It is strongly advisable for readers to explore the performance results of vectorization and observe the contrast with traditional loops.
Methods for vectorization include:
1. Using the `numpy.vectorize()` method.
2. Utilizing matrix multiplication methods available in NumPy.
As stated in the numpy.vectorize() documentation:
"The vectorize function is provided primarily for convenience, not for performance. The implementation is essentially a for loop."
It's important to note that using `vectorize()` in a nested manner can introduce complexity to the code and may lead to reduced code readability. Given that matrix multiplication inherently involves three nested loops, it is recommended not to employ the `np.vectorize()` method for this purpose. Consequently, we will proceed with implementing our code using the second method listed for vectorization.
In Python, there are several methods for vectorization, which means performing operations on entire arrays or matrices efficiently without explicitly writing loops. Here are two common methods for vectorization using NumPy:
The numpy matrix multiplication method allows you to vectorize a custom Python function so that it can be applied element-wise to NumPy arrays. It essentially wraps a Python function, making it compatible with NumPy arrays. Here's how to use it:
import numpy as np
# Define a custom Python function
def custom_function(x):
return x * 2
# Vectorize the custom function
vectorized_function = np.vectorize(custom_function)
# Create a NumPy array
arr = np.array([1, 2, 3, 4, 5])
# Apply the vectorized function to the array
result = vectorized_function(arr)
print(result) # Output: [ 2 4 6 8 10]
In this example, we define a custom function custom_function that doubles the input value. We then use np.vectorize() to create a vectorized version of this function, which we apply to a NumPy array arr. The vectorized function applies the doubling operation to each element in the array, resulting in the result array.
NumPy, a powerful library for numerical computations in Python, offers optimized methods for matrix multiplication, ensuring efficient execution of element-wise operations. Among these, the np.dot() and np.matmul() functions shine as versatile tools for matrix multiplication tasks.
Here's a practical example of how to leverage these NumPy functions:
import numpy as np
# Create two NumPy arrays
array_A = np.array([[1, 2], [3, 4]])
array_B = np.array([[5, 6], [7, 8]])
# Perform matrix multiplication using np.dot() or np.matmul()
result = np.dot(array_A, array_B)
# OR
# result = np.matmul(array_A, array_B)
print(result)
In this illustration, we initialize two NumPy arrays, array_A and array_B. We then employ either np.dot() or np.matmul() to execute matrix multiplication between these arrays. The outcome is a fresh NumPy array housing the matrix product.
When it comes to dealing with matrices in Python, particularly when managing substantial datasets, NumPy's specialized matrix multiplication methods are highly efficient and the recommended approach. These functions significantly enhance code readability and efficiency, ensuring seamless operations on arrays and matrices when working with numerical data.
Matrix multiplication in Python is a crucial mathematical operation with applications spanning various fields, including mathematics, physics, engineering, computer science, and data analysis. Python provides multiple methods for performing matrix transpose in Python, ranging from basic nested loops to optimized libraries like NumPy.
Understanding the fundamental principles of matrix multiplication, such as ensuring compatibility of matrix dimensions and following a systematic approach to calculate the product matrix, is essential. Moreover, leveraging vectorization techniques in libraries like NumPy can significantly enhance the efficiency of matrix operations in Python without NumPy.
1. When should I use vectorization for matrix multiplication?
Vectorization, especially in NumPy, should be used for matrix multiplication when working with large datasets or performing complex matrix operations. It takes advantage of optimized C and Fortran code, making operations faster and more memory-efficient.
2. Can I perform matrix multiplication using lists in Python without NumPy?
Yes, you can perform matrix multiplication using nested loops or list comprehensions in Python without NumPy. However, NumPy provides optimized functions for efficient matrix operations.
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Director of Engineering
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upGrad does not grant credit; credits are granted, accepted or transferred at the sole discretion of the relevant educational institution offering the diploma or degree. We advise you to enquire further regarding the suitability of this program for your academic, professional requirements and job prospects before enr...