Unit II: Least Squares, Determinants and Eigenvalues

Orthogonal Vectors and Subspaces

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

Vectors are easier to understand when they’re described in terms of orthogonal bases. In addition, the Four Fundamental Subspaces are orthogonal to each other in pairs.

If A is a rectangular matrix, Ax = b is often unsolvable. The matrix A_T_A will help us find a vector x̂ that comes as close as possible to solving Ax = b.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 4.1 in the 4th or 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you’re done.

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Course Info

Learning Resource Types

theaters Lecture Videos
grading Exams with Solutions
notes Lecture Notes
theaters Recitation Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations
groups Course Introduction
co_present Instructor Insights