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Linear Algebra +/- Graduate Linear Algebra


norules4suresh

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Hi, I have already taken a course in Linear Algebra (titled Algebra I), I am not quite sure whether it is a good idea to enroll in a graduate linear algebra course. Can someone tell me if this worth the time & effort or an utter waste of time? Thanks!

 

Linear Algebra

Matrix operations--vector spaces--linear transformations---the matrix of a linear transformation---linear operators and eigen values---the characteristic polynomial---orthogonal matrices and rotations.

 

Graduate Linear Algebra

Vector spaces, bases, linear transformations, matrices. Direct methods for solving linear equations--Gaussian elimination, positive definite systems, LU decomposition (by row-column operations), Banded systems (matrices whose nonzero entries are in a narrow band). Iterative methods for solving linear equations--Gauss-Seidel, successive over-relaxation. Orthogonal matrices, discrete least square problem, Gram-Schmidt method. Eigenvalues, reduction to standard forms, the QR algorithm, its implementation, generalized eigenvalue problem, Jordan canonical form, something on non-square matrices like decomposition of matrices by orthogonal transformations on domain and range (singular value decompositions). Introduction to optimization--gradient methods.

Edited by norules4suresh
made a typo
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I took a similar sounding class in my undergrad called Numerical Computation (or maybe it was Linear Programs), which sounds like it covers a lot of the same material. Nothings is a waste of time/effort if you enjoy learning math for the sake of learning it, but I have to imagine there would be a better class to take than this. I swear, I've learned like a dozen ways to solve Ax=b by hand, none of which I ever use because I can just type x=A\b into matlab. I guess it depends on what your alternative options are.
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Yes this one uses the text P.G. Ciarlet: Introduction To Numerical Linear Algebra And Optimisation.

 

Actually I'm interested in knowing whether this graduate LA is what the adcoms see as "Proof based LA" or the former course would suffice? I will choose this one only if I HAVE to, meaning, if the former course doesn't cover any specific required topic that has been covered in the latter.

 

Thanks!

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In that case I don't think this course is the best use of your time. Of course I don't know how the adcoms see things or what is really useful in a Phd program (since I'm a fellow applicant), but I think this sort of course is very much focused on the nitty-gritty of the numerical methods, going into far more detail than you'll ever need. Stuff like various matrix decompositions and canonical forms are interesting, but it's really more useful for pure mathematicians, computer science, or operations research. Your first LA course should be sufficient in the eyes of the adcoms. If you're looking for more math, I'm a big fan of fourier/spectral analysis, but I'm biased since I was an electrical engineer.
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What kind of applications does fourier analysis have to economics?

Fourier/Spectral analysis can be useful in econometrics, especially when looking at time-series data. Fourier transforms and related topics are the bedrock of signal processing, and time-series data are really just another type of signal. On a related note it's also useful in looking at financial data series (stock prices) as well. But it's a very obscure, advanced corner of econometrics I imagine.

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