<p>Many of you probably have the choice between linear algebra and applied linear algebra. Does anyone have any experience or insight into which one is easier, more interesting, etc.</p>
<p>Here are the course descriptions for my school:</p>
<p>MAT 343 Applied Linear Algebra.
Solving linear systems, matrices, determinants, vector spaces, bases, linear transformations, eigenvectors, norms, inner products, decompositions, applications. Problem solving using MATLAB.</p>
<p>MAT 342 Linear Algebra.
Linear equations, matrices, determinants, vector spaces, bases, linear transformations and similarity, inner product spaces, eigenvectors, orthonormal bases, diagonalization, and principal axes.</p>
<p>At most schools they have a linear algebra for math majors and one for engineering majors. The math major will have a lot of proofs and theory while the engineering one will be more focused on problem solving and applications. Which is more interesting will depend on your interests, but I'd say for most students the applied linear algebra willl be easier. Most engineering students take an applied linear algebra.</p>
<p>i took linear algebra my junior year in high school. the concepts are fairly abstract. based on the short description of applied linear algebra, i believe that the applied l.a. is easier.</p>
<p>The second choice (non applied) has a few more concepts, but the actual work should be less redundant and boring. Plus those concepts are generally reasonable. Of course depending upon how the two courses are taught, the theory one may require you to like proofs more.</p>
<p>Personally knowing everything on both lists, I'll take the dissenting opinion and take the second one as it teaches you more interesting (and not really difficult, not any more so than applications) things but generally far less boring things. Sorry to say, but generally you do get applications even in a theoretic linear algebra class, and generally most applications that can be covered (since they have to be brief) are generally on the boring side. But perhaps that's just me.</p>
<p>If you can do linear transformations, you can do similarity transforms. They're just a particular type of a transformation. (A transformation of a matrix M is say left multiplication by a matrix say T - well, a little more to it, but for now bear with this. Similarity is such that matrices M and K are similar if T<em>M</em>T^(-1)=K for some invertible (^-1 is the inverse) matrix T. Not much to it).
Diagonolization is just an application of linear transformations, and the reason transformations are really useful (say taking powers of a matrix is generally intensive, you can transform the matrix to a diagonal one [all 0 entries but diagonal ones], take that same power, and transform the result back into what you were working with before).
Orthonormal bases/principal axes is in a way applications about choosing your bases such that they end up being more convinient for you. One way to think about is units. Say you have a coordinate in say a two dimensional space (dimension 1 - location, dimension 2 - time) and you have a coordinate point. One way you could say x meters, y seconds. Alternatively (but more complicated), you can say x meters and seconds, y seconds. So for instance 2 meter 1 second OR 2 meter & second -1 seconds. The first example would be something like an orthonormal base (meter and second are totally independent and don't conflict with another), unlike the second example. Perhaps this is complicating it a bit too muhc, but should give some idea.</p>
<p>I have taken both flavors...and an extra one which I will explain also.</p>
<p>A more theoretical version of Linear Algebra as an undergrad math major (actually, the course was titled "Theory of Matrices") and and applied version as a graduate engineering student (aptly called Applied Linear Algebra).</p>
<p>The applied version was easier as it more or less touched on the concepts and immediately applied it to civil or EE type of problems.</p>
<p>Now the 3rd flavor I had was the most fun "Computational Linear Algebra" which included a lot of computational/programming techniques in Linear Algebra, Linear Programming and Operations Research.</p>
<p>I have taken a course in both, and the applied one was much more advance and included more advance topics, and more proofs. </p>
<p>In the applied class we did SVD, Discrete Fourier Transformation, Invariant Subspaces, and a few other topics that weren't even covered in the non applied class. Then again the non applied class was required for the applied class.</p>