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Foundations of Artificial Intelligence & Machine Learning

Licence
OPEN CC-BY-4.0
Authors
Nidhi Sharma, Honey Singh, Ajay Sharma, Deepak Dagar
Published
2026-07-28 · Zenodo
Language
eng
Length
37166 words
Type
narrative text
Open ↗ Download Open original ↗
Importance of Linear Algebra in AI and ML

Linear Algebra is essential because modern intelligent systems involve high-dimensional data and complex computations. Its importance can be seen in:

  • neural network calculations

  • computer vision systems

  • recommendation engines

  • natural language processing

  • robotics

  • optimization algorithms In deep learning, entire layers of neural networks operate through matrix transformations and vector calculations. Search engines, facial recognition systems, and autonomous vehicles all rely on mathematical structures rooted in Linear Algebra. Feature Representation Using Vectors In Machine Learning, real-world objects and observations must be converted into numerical forms before algorithms can process them. This process is known as feature representation. For example:

  • a person's age

  • income

  • education level

  • purchasing behavior may be converted into numerical feature vectors. Similarly:

  • words in language models

  • pixels in images

  • audio frequencies in speech systems can all be represented mathematically using vectors and matrices. This numerical representation allows machine learning algorithms to identify patterns computationally. Dimensionality in Machine Learning The term “dimension” refers to the number of features or variables present in data. For example:

  • a dataset containing height and weight has two dimensions

  • a dataset containing hundreds of medical attributes may contain hundreds of dimensions High-dimensional data is common in AI systems, especially in image processing and natural language applications. Linear Algebra provides mathematical tools for handling such complexity efficiently.