R Companion to Linear Algebra Step by Step, Chapter 2 section 3

November 23, 2019

[This article was first published on R – Detroit Data Lab, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Chapter 2 section 3 covers Linear independence.

In this post, I’ll continue writing R code to accompany linear algebra equations found in Linear Algebra: Step by Step, by Kuldeep Singh. For more information on the origins of these posts, see the first companion post

Section 2.3 – Linear Independence

To detect linear dependence in rows or columns, the simplest way I’ve found is by using the qr function to check rank. Unfortunately, rank is covered in section 3.5.5.

Example 2.13 can be completed with the code below, since we compare the output to what we know of the matrix. The rank is 3, and it’s a 3×3 matrix, so we have linear independence. First, establish A as the matrix, then transpose it in the qr function so we’re checking columns for linear dependence. The book later proves that row and column ranks are equal, but for the sake of this exercise, we’ll be sure to check columns.

A <- matrix(c(-3,0,2,1,1,0,0,-1,0), nrow = 3, byrow = TRUE)
qr(t(A), tol = NULL)

Example 2.14 is performed with the code below, interpreting similarly.

A <- matrix(c(2,-4,0,3,19,0,7,-5,0), nrow = 3, byrow = TRUE)
qr(t(A), tol = NULL)

To leave a comment for the author, please follow the link and comment on their blog: R – Detroit Data Lab.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Search R-bloggers


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)