Linear algebra is commonly used in computer science for machine learning, optimization, graphing algorithms, search engines, data organization, image processing, cryptography, and more. It allows input data like images or text to be represented as vectors and matrices that can then be transformed or manipulated through linear algebra operations to power applications like machine learning models, search result rankings, image filters, and encryption techniques.

1. Linear Algebra:
Applications in
Computer Science
By:
-Jacob L
-Richie

2. Common Applications of Linear Algebra
within Computer Science:
❏ Machine learning
❏ Optimization (data / code / processing)
❏ Graphing algorithms, projections and predictive models.
❏ Search engines and result order
❏ Grouping and data organization
❏ Image processing and facial recognition
❏ IP address design schemes
❏ Cryptography

3. Machine Learning
❖ Input and output:
➢ Input as vectors with various numbers to represent the
observed data, allowing for linear transformations or
various matrix operations to produce output.

4. Graphing Algorithms, Projections, and
Predictive Models.
❖ Predictive modeling and projecting given inputs:
➢ Matrices and matrix transformations allow for input data
to be projected into predictive models for various cases.
■ One particular example is Markov Chains.

5. Search Engines, Data Retrieval and
Result Order.
❖ Google’s PageRank algorithm:
➢ Developed using eigenvectors and eigenvalues to predict
useful websites based on input from previously searched
and clicked sites.

6. Image Processing and Facial
Recognition
❖ Image processing and changes such as sharpen, scaling,
shearing, blurring, and more:
➢ All of these operations can be done via multiplying and
manipulating matrices with values assigned to pixels.
➢ Also used for facial recognition software to determine
facial features.

7. Cryptography
❖ Matrix Transformations can be used for encryptions
➢ The product of an encryption matrix and a ciphertext
matrix
❖ Hill ciphers use linear systems
➢ Decryption through solving