Introduction
Linear algebra is a fundamental concept in mathematics that is widely used in various fields, including machine learning, data analysis, and computer science. In this article, we will explore the basics of linear algebra, focusing on matrix multiplication, and provide resources for further learning.
Matrix Multiplication: The Key to Linear Algebra
Linear algebra is all about matrices, and mostly about multiplying those matrices. If you were to remember only one thing about the topic, it would be this. To multiply two matrices, they have to be of certain shape. Specifically, the number of columns in the first matrix must be the same as the number of rows in the second matrix. That’s because we’re multiplying rows by columns, and they have to be of the same length.
For example, consider the following matrices:
(1000, 4) * (4,50) => (1000, 50)
Note how the resulting matrix has the same number of rows as the first one and the same number of columns as the second one. This knowledge of shape requirements is very helpful in debugging.
Linear Algebra Resources
If you would like to learn more about linear algebra, there are many courses and books about the topic, many of them free. For beginners, Jeff Chasnov’s Matrix Algebra for Engineers seems like a good choice. The videos are available on YouTube, and the booklet is linked in the descriptions. For starters, you can check the video about matrix multiplication.
Jeff Chasnov offering you a blue pill and a red pill
For a deeper dive Gilbert Strang’s lectures are a classic and a gold standard. Strang also has a few books.
For doing exercises, one could use sympy in addition or even instead of pen and paper. Sympy seems to be more geared towards educational use than numpy and features operations you won’t find in numpy, such as computing matrix determinants, for example.
In [1]: from sympy import *
In [2]: A = Matrix([ [1,2,3], [4,5,6], [7,8,9] ])
In [3]: A
Out[3]:
Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
In [4]: A.det()
Out[4]: 0
There is even a more advanced linear algebra course that uses sympy with code snippets embedded on the webpage in a notebook fashion.
Credit: A meme page to check every time MatLab crashes
Conclusion
In conclusion, linear algebra is a fundamental concept in mathematics that is widely used in various fields. Matrix multiplication is a key concept in linear algebra, and understanding the shape requirements is crucial for debugging. There are many resources available for learning linear algebra, including free courses and books. We hope this article has provided a good starting point for your linear algebra journey.
Frequently Asked Questions
Q1: What is the key concept in linear algebra?
The key concept in linear algebra is matrix multiplication, which requires the number of columns in the first matrix to be the same as the number of rows in the second matrix.
Q2: What are some good resources for learning linear algebra?
There are many resources available for learning linear algebra, including free courses and books. Some popular resources include Jeff Chasnov’s Matrix Algebra for Engineers, Gilbert Strang’s lectures, and sympy.
Q3: What is sympy?
sympy is a Python library that is used for symbolic mathematics. It is particularly useful for linear algebra and features operations that are not available in numpy, such as computing matrix determinants.
Q4: What is the purpose of debugging in linear algebra?
Debugging in linear algebra is crucial for identifying and correcting errors in matrix multiplication. Understanding the shape requirements of matrix multiplication is essential for debugging.
Q5: Are there any advanced resources for learning linear algebra?
Yes, there are many advanced resources available for learning linear algebra, including more advanced courses and books. One example is the linear algebra course that uses sympy, which features code snippets embedded on the webpage in a notebook fashion.
