From linear algebra to machine learning

By Omar Trinidad Gutiérrez Méndez

Elevator Pitch

Math is a crucial skill for people who are interested in Data Science and Machine Learning. In this tutorial, I want to show how linear algebra is related to machine learning and why is essential to grasp math concepts to understand data science. We will see the role of Python in this relationship.


Math is a crucial skill for people who are interested in Data Science and Machine Learning. Until now, most of the people who are doing Data Science have a strong background in math, usually, people with master or Ph.D. degrees. However, this fact seems to change in the next years, after the hype of Machine Learning we are facing a process of democratization. Now the door of Data Science is open for everyone.

To “truly madly deeply” understand how the machine learning algorithms work we need to understand some mathematical concepts. In this tutorial, I would like to share my experience with the process of learning some of those concepts.

What I want to do is build a bridge between those concepts and Python, more specifically, SciPy and NumPy and TensorFlow. The talk is, basically, just another tutorial about vectorization, in this case, oriented to understand and implement machine learning algorithms and the mathematical foundation that supports it.


  • Review of linear algebra: A summary of essential linear algebra, concepts and the explanation with NumPy: scalars, vectors, matrices, tensors, multiplication of vectors, inner products, vector spaces, linear transformations, etc.
  • Review of machine learning: A review of essential machine learning, concepts that are related to mathematical concepts: classification, dimensionality reduction, etc.
  • Optimization: Analytical vs. numerical solutions. This part has too many formulas, well, not too many.
  • Vectorization: Numpy and TensorFlow.
  • Small practical cases (from scratch)
    • Linear regression
    • Feedforward neural networks
    • Dimensionality reduction: LDA and PCA.