Linear Algebra or Matrix Algebra

[peacejc]

I am going to apply a Phd Degree in Economics for 2011-2012.
I am interested in studying International Trade.

I have a question about math courses. I am going to take an Advanced Calculus (Cal 5) this coming semester.
I am wondering if I need to take Linear Algebra which is a required course in most schools.
Actually, I took Matrix Algebra instead of Linear Algebra, also other math courses (Cal 1-4, set theory, probability).

In this case, Should I really need to take a Linear Algebra to get an admission from a Phd degree ?
I think it is more important to get a good GPA on Advanced Cal than to take Linear Algebra.
Do you guys agree with this?

Thank you for spending your time
and I would appreciate your answer.

[The MAN]

Taking LA couldn't hurt. Also, you may want to look into Real Analysis. Those are the two biggies this board usually recommends (I haven't really seen much emphasis on Calc 5/Advanced Calc).

I'm sure someone with a better grasp of math classes will give you more astute advice than me.

[kevinp123]

Taking LA couldn't hurt. Also, you may want to look into Real Analysis. Those are the two biggies this board usually recommends (I haven't really seen much emphasis on Calc 5/Advanced Calc).

I'm sure someone with a better grasp of math classes will give you more astute advice than me.

Advanced Calc is Real analysis at a lot of schools. Same class, different name. Perhaps a bit tamer, but that is probably due to the school, not the name of the class.

In regards to the question, depending on how high you are aiming, a lot of schools require linear algebra but not adv. calc. So check the requirements for whatever schools you plan on applying to.

[TomRod]

If you're working through multivariate analysis (the typical subject matter for the fifth semester of calculus), then you are getting most of the linear algebra you will need. Advantages of taking linear algebra vary widely. Make sure to take the course from an applied mathematician. It helps also to ensure the course makes it through singular value decomposition.

[_nanashi]

Matrix Algebra and Linear Algebra are generally viewed as the same course. The predominant difference being that many departments consider Linear Algebra to be a more theoretical treatment of the material. If you've had matrix algebra and are taking a 2dn semeste undegrad analysis course (advanced calculus), I would not waste my time taking anotehr linear algebra course. Actually I think you made a better move in the long hall by taking Matrix Algebra. Econometrics benefits students who have proficiency in elementary matrix operations, and the properties of inverse matrixes, transposes, etc. Something that your likely to pay more attention to matrix algebra than linear algebra. (Which probably spends a bit more time on things like what constitutes a space, basis, span etc.)

[TomRod]

Matrix Algebra and Linear Algebra are generally viewed as the same course.

I respectfully disagree with this--in my experience, Matrix Algebra oftentimes incorporates elements of group and ring theory.

[corolla09]

Well I've never heard the term Calc-5 before. Nevertheless...Linear Algebra is required almost everywhere. If Matrix Algebra is the more advanced course, as mentioned above, it maybe contain some Ring/Group/Ideal Theory, much of which is directly related to economics but the techniques are. So whatever Real Analysis and Linear Algebra are called are you school take them at a minimum for your phd application.

[_nanashi]

I respectfully disagree with this--in my experience, Matrix Algebra oftentimes incorporates elements of group and ring theory.

I repsectfully disagree with your disagreement. All of the institutions I've been with have treated matrix algebra as how I am describing. Essentially Linear Algebra was required of students who planned to enter into a pure mathematics streaming, while matrix algebra was generally intended for engineers or statistics tracks. I took the course 3 times owing to the fact that matrix algebra didn't transfer between the various institutions I have been affiliated with. In addition a google search of the term matrix algebra course yields several courses that look like linear algebra, or titled linear algebra, or whose syllabuses that include an intro to linear algebra book. (e.g. MIT, Cornell, Carnegie mellon, Hofstra, Uiowa)

[asquare]

I repsectfully disagree with your disagreement. All of the institutions I've been with have treated matrix algebra as how I am describing.

Er, you made a generalization: you said that linear algebra and matrix algebra are "generally" viewed with the same course. That may or may not be true. It's subject to disagreement. TomRod described his specific experience. He said, "in my experience...". So what are you disagreeing with? Are you saying he didn't describe his own experience accurately? You might think his experience isn't representative, but it's silly to disagree that it is his experience.

I think the lesson to draw from this is that different schools use the terms to cover different classes. To figure out which class is the most appropriate for a student who wants to get a PhD in economics, it's necessary to read the description, not just the class name. Michigan has separate undergraduate classes named "linear algebra" and "matrix algebra." The former is a 200 level class and the latter a 400 level class. Despite that, the higher numbered "matrix algebra" class would probably be more useful to someone who wanted to do a PhD in economics:

Content: Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, Eigenvalues and Eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.
Alternatives: Math 419 (Lin. Spaces and Matrix Thy.) is an enriched version of Math 417 with a somewhat more theoretical emphasis. Math 217 (Linear Algebra) (despite its lower number) is also a more theoretical course which covers much of the material of 417 at a deeper level. Math 513 (Introduction to Linear Algebra) is an honors version of this course, which is also taken by some mathematics graduate students. Mathematics concentrators are required to take Math 217 or Math 513.

[dreck]

Yeah, I'd guess the Linear Algebra class is theoretic and the Matrix Algebra one more computational. But that doesn't mean that some departments don't do it the other way around. My courses were called Linear Algebra (the computational one), and Abstract Linear Algebra (which was crosslisted with a Masters-level class). But we did cover some of the theory in the former, rather than pure computation.
Fact is, if you've had a pretty thorough class in computation using Matrices, then you've got the tools and signalling stuff you need for a PhD in Economics. If you have an inkling about doing Econometric theory, though, you'd benefit from a more abstract understanding of Linear/Matrix/Whatever Algebra.