Applications of Linear Algebra in Computer Science
Computer Science in its essence contains a lot of logic and algorithms. It is a discipline
that focuses on the complexity and process of the computations they make. With this in mind,
one of computer science’s foundations is mathematics. It is integrated with the field in a number
of ways. It is used in the development of algorithms, data science employs statistics, and
discrete math helps in the development of the logic of a program.
One significant branch of mathematics that is essential to computer science is Linear
Algebra. Matrix computations are often seen and implemented in developing computer
programs and Algebra is also used in evaluating codes, processor optimization, and more. It is
considered the backbone for a lot of concepts like computer graphics, machine learning, image
recognition, cryptography, and more. In this paper, I aim to explore the importance of linear
algebra and dive deeper into the different applications it brings in the field of computer science.
One application for linear algebra is cryptography. Cryptography refers to the
encryption and decryption of sensitive information derived from mathematical concepts to
transform messages in ways that are hard to decipher (K. Richards, 2020). If we want to encrypt
a message, the message and a cipher matrix are required. We also need to convert the message’s
letter into its numerical value and group them into a 3x1 matrix. Here is an example:
1 −1 0
𝐴= [1
0 −1]
−6 2
3
𝑀𝑒𝑠𝑠𝑎𝑔𝑒: 𝑺𝑵𝑰𝑻𝑪𝑯
𝑆 = 19, 𝑁 = 14, 𝐼 = 9, 𝑇 = 20, 𝐶 = 3, 𝐻 = 8
𝐴𝑢𝑔𝑚𝑒𝑛𝑡𝑒𝑑 𝑀𝑎𝑡𝑟𝑖𝑥 = [19
14
9], [9
20 3]
After obtaining the newly formed matrix, multiply the cipher matrix with the
augmented matrix. The result will now be your new encrypted message. If we have to decrypt,
we only require the inverse of the given cipher matrix and the encrypted matrix. We multiply
those two matrices and convert the numerical to its alphabet form and we should see the
message.
[19
14
[9 20
1 −1 0
9] [ 1
0 −1] = [−21
−6 2
3
1 −1 0
3] [ 1
0 −1] = [11
−6 2
3
𝑬𝒏𝒄𝒓𝒚𝒑𝒕𝒆𝒅 𝑴𝒂𝒕𝒓𝒊𝒙 = [−21
−1 13]
−3 −11]
−1 13], [11
−3 −11]
−2 −3
𝐴−1 = [−3 −3
−2 −4
−1
−1]
−1
[−21 −1 13] −2 −3
[−3 −3
[11 −3 −11]
−2 −4
𝑫𝒆𝒄𝒓𝒚𝒑𝒕𝒆𝒅 𝑴𝒂𝒕𝒓𝒊𝒙 = [19 14
9], [9 20
−1
[19 14 9]
−1] =
[9 20 3]
−1
3] = [𝑆 𝑁 𝐼], [ 𝑇 𝐶 𝐻] = 𝑺𝑵𝑰𝑻𝑪𝑯
There are many uses of cryptography in technology, and we do not even realize that we
are utilizing such kind of concept. One function is that cryptography is the one responsible for
keeping the emails we send and receive secure and private. Prasanth Reddy (2019) defined
email encryption as a method of securing the content of emails from anyone outside of the
email conversation looking to obtain a participant’s information. Email encryption works by
providing two unique keys to one particular email address. The public key, which is used to
encrypt the message, and the private key, which is used to decrypt the email. When an email is
sent, the public key encrypts the message into a complex, undistinguishable mix. Only the
person with the correct email and private key will be able to decrypt and read the message. As
a computer science student, this is very significant because we should be knowledgeable and
aware of how emailing may look simple on the outside but in reality, it involves a lot of linear
algebra particularly on cryptography. When we are assigned to code an application that may
contain users’ sensitive information, we must keep in mind how we can make it safe and
protected because once the security has been breached, dire consequences will emerge, and no
programmer would want to shoulder that responsibility.