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.

[Guest _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.

[Guest _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.

[Guest _nanashi]

You might think his experience isn't representative, but it's silly to disagree that it is his experience.

I'm not disagreeing with his experience. I'm disagreeing with this part of his statement.

Matrix Algebra oftentimes incorporates elements of group and ring theory.

 

Again I know a school can be an outlier with regards to naming conventions, for example at my undergrad institution Functional Analysis is called Real Analysis II, but I don't expect that to be normal at most schools and people to assume that to be a possibility. Generally when you state that I've taken Calculus or Matrix Algebra, most people would assume the courses covered certain content which is standard. I think that most people would assume a course on matrix algebra to be nearly identical in content to an intro to linear algebra course. If that weren't the case a google search of matrix algebra would not bring up several pages that are related to introductory linear algebra.

[wtflolrofld]

There's not such thing as theoretical math. It's either pure math or applied math.

At my school, Linear Algebra is offered only in first year courses (standard level or honors), while the Matrix Algebra course is at third/fourth year level.

Last year, I asked a professor who has a Ms in mathematics and Phd in economics from a top 15 US program for course suggestions. He only suggested 3 courses: Analysis I, II and the said Matrix Algebra class. Later I found that the couse is a requirement of the Bachelor of Statistics degree at my school. Apparently it has a lot to do with econometrics, too.

I think while Linear Algebra is almost assumed knowledge of any Phd student, Matrix Algebra is one of the better math electives that you should look into.

[asquare]

I'm not disagreeing with his experience. I'm disagreeing with this part of his statement.

Matrix Algebra oftentimes incorporates elements of group and ring theory.

You are deliberately taking that statement out of context. The original statement was, "in my experience, Matrix Algebra oftentimes incorporates elements of group and ring theory." His experience may not be representative, but it is silly to dispute that it is his experience and misleading to drop the "in my experience" part of the quote as you do in your post.

[Guest _nanashi]

You are deliberately taking that statement out of context. The original statement was, "in my experience, Matrix Algebra oftentimes incorporates elements of group and ring theory." His experience may not be representative, but it is silly to dispute that it is his experience and misleading to drop the "in my experience" part of the quote as you do in your post.

Actually I rather feel like your taking what I am writing out of context, and twisting it with your own subjective interpretations going as far as to interpret what my intentions are.

 

My issue is clearly one of whether a Matrix Algebra course generally is substantially different in content or topics from linear algebra. I think I've been pretty consistent on that line of discussion. It has nothing to do with his personal experience, the term he used was that it is oftentimes common for matrix algebra to cover group and ring theory. No I don't think this is representative, and my issue is directly to do with the fact that he indicates that it is common occurrence.

[asquare]

Actually I rather feel like your taking what I am writing out of context, and twisting it with your own subjective interpretations going as far as to interpret what my intentions are.

 

My issue is clearly one of whether a Matrix Algebra course generally is substantially different in content or topics from linear algebra. I think I've been pretty consistent on that line of discussion. It has nothing to do with his personal experience, the term he used was that it is oftentimes common for matrix algebra to cover group and ring theory. No I don't think this is representative, and my issue is directly to do with the fact that he indicates that it is common occurrence.

He said that matrix algebra often incorporated group and ring theory in his experience. He gave people the information necessary to evaluate his statement by saying that it was based on his own experience. That phrase is critical and dropping it from the quote changed the meaning of the statement.

 

At any rate, this conversation is silly verging on absurd and certainly not hopeful to the OP, whose question I hope was answered long ago. I'm done with this.

[TomRod]

Any course dealing with R^n x m (or C^ n x m) that takes you up to eigenvalues/eigenvectors, singular value decomposition/factor analysis, and the Gram-Schmidt orthogonalization process is probably sufficient to get you to an acceptable level of linear algebra.