Applications of linear algebra in computer science

WELCOME TO OUR PRESENTATION ON
“APPLICATION OF LINEAR ALGEBRA
IN CSE”
We are “RAINBOW WARRIORS”

Name: ID:
MD. Atikur Rahman 181-15-2024
MD. Najmus Shakib 181-15-1913
MD. Aminul Islam 181-15-1888
MD. Rasel Ahmed 181-15-2060
Jakirul Hasan 172-15-1615
Group Name : RAINBOW WARRIORS
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 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.
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 History of Linear Algebra
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
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• 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.
 Why Linear Algebra is important ?
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 Uses of Linear Algebra in CSE
 Linear Algebra in computer science can
broadly divided into two categories:
Here you're dealing with 2-, 3-, or 4-
dimensional vectors and you're concerned with
rotations, projections, and other matrix
operations that have some spatial
interpretation. This is the kind of linear algebra
that comes up, for example, in computer
graphics and physics simulations.
1) Linear Algebra for spatial quantities.
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Here you're dealing with vectors in high-dimensional
spaces that have no particular spatial interpretation
and you're interested in matrix decompositions and so
on. This domain includes signal processing, statistical
machine learning, and compression.
2) Linear Algebra for statistics.
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 Linear Algebra in Network Models
Determine the currents I1, I2, and I3 for the
following electrical network:
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 Linear Algebra in Cryptography
Encryption and decryption require the use of
some secret information, usually referred to as
a key. Example Let the message be
“PREPARE TO NEGOTIATE”
We assign a number for each letter of the
alphabet. Thus the message becomes:
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Since we are using a 3 by 3 matrix, we break the enumerated
message above into a sequence of 3 by 1 vectors:
By multiplying encoding matrix to this matrix
we will encrypt the msg.
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Now to decrypt the msg we have to multiply
this matrix to Inverse of encoding matrix
• The inverse of this encoding matrix, the
decoding matrix, is:
• Multiplying again by this matrix we will get our Msg.
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 Importance of Linear Algebra in various category
Very important in Computer Vision for:
 Camera modeling;
 Epipolar geometry;
 Calibration and self-calibration;
 Pose estimation;
 Structure-from-motion;
 And many other things.
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Very important in Machine Learning. For example :
 Dimensionality reduction;
(e.g. Principal component analysis)
 Clustering;
 Classification;
 Prediction;
 Recommender systems
(e.g Collaborative filtering) etc..
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Matrix in Neural Network

Linear Algebra is crucial to:
 Audio, video and image compression, including MP3, JPEG and
MPEG video.
 Modulation and coding, including convolutional codes and Wi-Fi,
Gigabit Ethernet, HDTV and the GPS.
 Signal processing, including the Fast Fourier Transform and
autotune!
 Statistics and machine learning, including something as far a field
like automated trading in the financial markets
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 In computer graphics every element
is represented by a MATRIX.
 Linear Algebra Computer Graphics
 All images can be represented in matrix format.
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 Linear Algebra in video games
Linear algebra is the study of vectors. If your game
involves the position of an on-screen button, the
direction of a camera, or the velocity of a race car, you
will have to use vectors. The better you understand
linear algebra, the more control you will have over the
behavior of these vectors.
In games, vectors are used to store positions, directions,
and velocities. Here are some 2-Dimensional examples:
The position vector indicates that the man is standing
two meters east of the origin, and one meter north. The
velocity vector shows that in one minute, the plane
moves three kilometers up, and two to the left. The
direction vector tells us that the pistol is pointing to the
right.

 Conclusion
 There are so many application of Linear Algebra in Computer
Science. From simple circuit solving to large web engine
algorithms. The heart beat of computer science is in linear
algebra especially in the generation and formation of computer
coding schemes .
 That's the study of matrices especially identity matrices under
linear algebra is key to computer coding schemes generation and
formation unlike what we have in computer engineering. These
are programming primitives normally encapsulated into
programming languages and translators design.
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Therefore linear algebra is a course in mathematics which is a subfield in
theoretical computer science. Of course linear algebra is also useful in
secondary programming, like in computer graphics, database systems
and IP address design, etc.
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Applications of linear algebra in computer science

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