Can you use R to replace MATLAB?
Yes.
I used MATLAB for years but switched primarily to R in the last 3 years. At this point, they have much more in common than not. It partially depends on your field and use-case. And as Spencer Graves said previously, it also depends on which "church you happen to frequent". It's best if you look at the MATLAB toolkit vs. CRAN for a specific task before you decide.
A similar question asked on R-Help a few years ago and again more recently. David Hiebeler (at the University of Maine) maintains an extensive R/MATLAB comparison, and is the best reference on the subject. You can also review this comparison of basic functions.
Here are some of the things that I've observed in the past, none of which should be deal-breakers.
- Generally, MATLAB has a better programming environment (e.g. better documentation, better debuggers, better object browser) and is "easier" to use (you can use MATLAB without doing any programming if you want). Simulink allows you to visually program by connecting blocks in graphs. REvolution R is addressing some of these differences by providing a better IDE with improved debugging, but it's still a step behind.
- MATLAB is a little faster with the normal configuration (see this benchmark for an example), although there are things that can be done to improve R performance if that becomes an issue.
- Since it's commercial, it also arguably has more "products" (in the sense of integrated add-ons) and support (but you pay for it). See the product list. For instance, it has things like the MATLAB compiler which creates executable MATLAB programs that can be deployed.
- So far as packages/toolkits are concerned, MATLAB has much more support for the physical sciences while R is stronger for statistics, which is not to say that the other can't perform these tasks. And they can both be easily extended.
So, if ease-of-use isn't a primary concern (and there's no other business reason to avoid using an open-source tool), then I think that there's a real case to be made for using R. It has a very strong community around it (the R mailing lists are amazing), is rapidly developing (see CRAN), and it's free (which isn't a small issue!).
Edit: I would just add one further point to this: the book "Functional Data Analysis with R and MATLAB" includes a chapter on the "Essential Comparisons of the Matlab and R Languages". This covers some important syntax differences (such as the interpretation of a dot, or the meaning of square brackets []). The book itself is well worth reading for anyone interested in functional programming (in either language).