L4.1 - Vector spaces, subspaces for AI and Machine Learning

Vector spaces and subspaces form the mathematical foundation of Machine Learning and AI, enabling efficient representation of data, features, and models. They provide a structured way to manipulate high-dimensional data, ensuring consistency in transformations. The dot product space introduces geometric intuition, enabling similarity measures and optimization techniques like gradient descent. In these spaces, basis vectors define fundamental directions, and new vectors emerge from their weighted combinations, allowing flexible transformations and dimensionality reduction. Understanding vector spaces is crucial for mastering linear regression, PCA, neural networks, and beyond—driving AI’s ability to learn, generalize, and make intelligent decisions. 🚀

00:00 Introduction and relation with machine learning

01:11 What is a vector space?

01:28 What do we mean by structures and objects?

01:52 Vector space addition properties

02:57 Vector space scalar multiplication

03:31 Inner product space

04:39 Insights from mathematics for motivation

06:37 What is a vector subspace?

06:53 Properties of vector subspaces

07:09 Example of 1D vector subspace in 2D ambient space

08:03 Example of 2D vector subspace in 3D ambient space

09:27 Quiz

#machinelearning #ai #datascience #vectorspaces #subspaces #dotproduct #dimensionalityreduction #acharyaai

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