Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Rank

The video tutorial introduces the concept of linear least squares in data science, explaining how vectors in Euclidean space can be used to form linear combinations. It discusses the setup of linear systems, the conditions for their solutions, and the concept of column space. The tutorial also covers scenarios where exact solutions do not exist, leading to the need for approximate solutions using Euclidean distance. The linear least squares problem is formulated as minimizing the norm of residuals, with a focus on understanding matrix products and vector spaces.

What is the goal when working with vectors in Euclidean space as described in the text?

Explain the significance of the linear combination of vectors in relation to producing another vector.

What does it mean if a linear system has no solution in the context of column space?

Describe the concept of residuals in the context of linear least squares.

What is the relationship between the norm of residuals and the goal of minimizing it?

How is the problem of finding an approximate solution formulated in linear least squares?

Discuss the importance of understanding vector spaces in solving linear least squares problems.