Strang is an MIT math professor who has written another widely used linear algebra textbook (CUNY Library/Amazon), and so the course follows his book. One of the sections of his book is called “The Four Fundamental Subspace.” You can find a pdf paper by Strang about these four subspaces here, which introduces the subspaces in the first paragraph:

“The expression Four Fundamental Subspaces has become familiar

to thousands of linear algebra students. Those subspaces are the column space and the nullspace of *A* and *A^T* [i.e., transpose of *A*]. They lift the understanding of [the matrix equation] *A x = b* to a higher level–a subspace level. The first step sees

Here is Strang’s lecture–it’d be worth setting aside an hour to watch it:

]]>The Invertible Matrix Theorem ties together just about all the concepts we’ve covered in the course so far. Here are some resources to supplement the textbook and our discussion in class:

- Extended statements of the IMT here and within the Invertible Matrix entry on Wikipedia (i.e., they include a bunch of additional equivalent conditions, which deal with concepts we will cover later in the course, like the column and null spaces, determinants, and eigenvalues.
- A detailed proof of the IMT, written up by another CityTech faculty member who has taught this course: “Using pivot positions to prove the Invertible Matrix Theorem in Lay’s Linear Algebra“
- A set of slides that go along with the treatment of the IMT in the the textbook

I’ll be using this site and the associated course profile page on OpenLab for communicating with you about the course, and occasionally directing you to online resources that might help you. You can also communicate with me & your classmates via the comments to posts here, and via the discussion forums on the course profile page.

The first thing you should do is set up an account on OpenLab if you haven’t already done so. Here are some instructions pulled from this post by another math prof on how to do so:

You will need to do two things:

- If you have not used the openlab before, you must first create an account. You will need access to your citytech email address for this. Detailed instructions for signing up on the OpenLab can be found here.
- Once you have created an account on the OpenLab, log in and then join this particular course, Spring 2013 – MAT 1272 Statistics – Reitz [for our course, join MAT 2580 Linear Algebra – Spring 2013 – Ganguli]. To do this, first click the “Course Profile” link at the top left of this page (just under the picture) [which I’ve also linked to above]. Then click the “Join Now” button, which should appear just underneath the picture of the blackboard.

Problems with the OpenLab or with your CityTech email:Please let me know if you run into any problems registering or joining our course (send me an email, jreitz@citytech.cuny.edu). I also wanted to give you two resources to help out in the process:

1. For problems with your

citytech email account, contact theStudent Computing Helpdesk, either in person, by phone, or by email:

Student Computing HelpdeskLocation: Namm First Floor – Information Booth

Hours: Monday, Wednesday & Friday: 9:00am – 5:00pm

Tuesday & Thursday: 9:00am – 6:00pm

Phone: 718.260.4900

E-mail: Studenthelpdesk@citytech.cuny.edu2. For problems

registering for the OpenLab, contact theOpenLab admin team, either by email at openlab@citytech.cuny.edu, or by following this link.

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