Quote of the day: You can’t learn too much linear algebra

Benedict Gross, Professor of Mathematics at Harvard said in his E-222 lecture: ‘You can’t learn too much linear algebra’.

If you read my WordPress pages in Signals and Systems, I’m trying a new approach to explain the materials done under the classical approach in a much more compact way using basic ideas in linear algebra.

Linear algebra is fun and easy to learn (at intro levels), once you get used to the fact that it’s a carefully picked set of restrictions that most physical problems boils down to. In high school algebra, it’s disguised as ‘method of detached coefficients’ when you solve systems of simultaneous equations.

Once you model your problem into linear equations (the hardest part), you will see the equivalence (or mathematically equivalent analogs) of different problems ranging from economics to circuits and mechanics. The beauty of the ‘detached coefficients’ approach separates the context of the problem from its mathematical structure as the application specific variables are often grouped as a vector (or matrix) that you deal with as a unit. In fact, most problem boils down to this:

    \[ \bf{Ax = b} \]

It’s your job to construct \bf{A}, \bf{x} and \bf{b} and tell people what they mean.

I agree with Gilbert Strang, Professor of Mathematics at MIT that it’s time to make linear algebra the standard curriculum over calculus. Digital control used to be a very advanced graduate class, but after a few decades, it’s undergraduate material. Linear algebra has very few knowledge dependencies (hard pre-requisites), so it’s great material to teach at any level.

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