Linear algebra is foundational in computer science and engineering, heavily used in technologies like digital imaging, gaming, and web searching. It simplifies complex problems by transforming them into matrix form, which is critical in data science and machine learning, where data is often represented as matrices. Understanding linear algebra enhances intuition for algorithms, enables better model development, and allows for experimentation in data science.

1. Application of Linear Algebra in
Computer Science and
Engineering
Abdul Motaleb Foysal
Salma Akter
Najah Nur

2. Introduction
When you take a digital photo with your phone or
transform the image in Photoshop, when you play a
video game or watch a movie with digital effects, when
you do a web search or make a phone call, you are
using technologies that build upon linear algebra.
Linear algebra in turn is built on two basic elements,
the matrix and the vector.

3. • The study of linear algebra first emerged from the
introduction of determinants. Determinants were
considered by Leibniz in 1693, and subsequently, in
1750, Gabriel Cramer used them for giving
solutions of linear systems, now called Cramer's
Rule. Later, Gauss further developed the theory of
solving linear systems by using Gaussian
elimination. The study of matrix algebra first
emerged in England in the mid-1800s. Linear
algebra first appeared in American graduate
textbooks in the 1940s and in undergraduate
textbooks in the 1950s.

4. • • Linear algebra is vital in multiple areas of
computer science because linear equations
are so easy to solve.
• • It converts large number of problems to
matrix and thus we solve the matrix.

5. • Linear Algebra, mathematical discipline that
deals with vectors and matrices and, more
generally, with vector spaces and linear
transformations. Unlike other parts of
mathematics that are frequently invigorated
by new ideas and unsolved problems, linear
algebra is very well understood. Its value lies
in its many applications, from mathematical
physics to modern algebra and coding theory.

6. • There are many application sectors in CSE.
On this slide we will discuss about the first four topic.

12. Graph: Linear Algebra on Data Science
• Linear Algebra is a branch of mathematics
that is extremely useful in data science.
Linear algebra is the most important math
skill in machine learning. Most machine
learning models can be expressed in
matrix form. A dataset itself is often
represented as a matrix

14. I consider Linear Algebra as one of the foundational blocks of computer science and
engineering . You cannot build a skyscraper without a strong foundation, can you? Think
of this scenario:
You want to reduce the dimensions of your data using Principal Component Analysis
(PCA). How would you decide how many Principal Components to preserve if you did not
know how it would affect your data? Clearly, you need to know the mechanics of the
algorithm to make this decision.
With an understanding of Linear Algebra, you will be able to develop a better intuition for
machine learning and deep learning algorithms and not treat them as black boxes. This
would allow you to choose proper hyperparameters and develop a better model.
You would also be able to code algorithms from scratch and make your own variations to
them as well. Isn’t this why we love data science in the first place? The ability to
experiment and play around with our models? Consider linear algebra as the key to
unlock a whole new world.
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