Current offering: EE5120, July — Nov 2026 — lecture-by-lecture coverage, evaluation schedule and announcements are on that page.

Course notes

Below is a set of course notes developed for a first graduate course in linear algebra, taught at IIT Madras as EE5120. The audience is a mix of senior undergraduate and beginning graduate students in engineering. The treatment follows the topic order used in class, which is not the same as that of any single textbook; Gilbert Strang’s book (GS) is the reference we point to, but the notes carry more by way of proof and rigour than the book does, and they do not repeat an idea with numerical examples once it has been established.

The course is built around two equations, \(Ax=b\) and \(Ax=\lambda x\). Almost everything we do is an attempt to understand one of them properly.

  1. Linear system of equations

  2. Vector spaces

  3. Orthogonality

Companion pages with Matlab/Octave commands for working through the material:

  1. Chapter 1 Matlab resources

  2. Chapter 2 Matlab resources

  3. Chapter 3 Matlab resources

Note: In case you find that some of the math fonts in the above notes do not load correctly, try right clicking the missing font, then "math settings", then "math renderer" and then "Common HTML" to see if it is rendered correctly.

Outline of the course

  1. Linear system of equations

  2. Vector spaces

  3. Orthogonality

  4. Eigenvalue problems

  5. Positive definite matrices

  6. Singular value decomposition

Notice

  1. You may use these notes for academic purposes with an attribution to me and this page.

  2. You may not re-post this content anywhere without explicit permission from me.

Reference material

  1. Linear Algebra and its Applications, Gilbert Strang, 4th ed. Keyword GS

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