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Topic-Specific
Why Learn Linear Algebra? What is it?
- 2014.01.21 - Math Vista - Why Linear Algebra?
- Great video. He says that linear algebra is just about having functions that have more than one input and/or output variable. He gives a bunch of examples:
- Given a time, return an X and Y coordinate
- Given an X and Y coordinate, return a Temperature and Pressure
- Tom:
- I've always viewed linear algebra as the natural extension of coordinate geometry -- linear equations are lines and planes and so solving these things is the same thing as finding intersections. Matrix transformations are the same things as dilations/rotations/etc -- very natural things to want to do to geometric objects. A lot of the computational (let's solve these systems, rather than draw pictures) approaches don't start off with this motivation (it does, after all, take time), but I think intuition benefits from it.
What's the cross-product?
- 2014.01.21 - Math Vista - The Cross Product
- another great video from this guy. He says that when you have a complicated line, it's often helpful to deal with a simplification of it to a straight line. Similarly, when you have a wavy 2D shape, it's often helpful to deal with a simplified flat 2D surface. And so on for higher-dimension shapes. Now, when you have a straight line you know exactly its slope if you know the line perpendicular to it. And if you have a 2D flat surface you know the slope in BOTH directions if you know the vector that's "normal to" the surface. And so on for higher dimensions. So getting that normal vector is a way of getting a simple shorthand for the whole surface.
