Just wrote my Linear Algebra 2 exam yesterday at UWaterloo. Admittedly, I had more of a love and hate relationship with these 2 courses, but near the end and looking back at them, I did really enjoy them. Seeing these videos and actually being able to understand what's going on just makes me realize how far I've come, and if I could go back in time I would definitely take them again.
i wish i had learned it like that, but instead, the first time i saw it, was just proving hard theorems about existence of eigenvalues and eigenvectors, or orthonormal basis of eigenvectors or something like that, never had the time to actually play with the characteristic polynomial and find actual eigenvalues, great video
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Great lecture! saw you at the duocon and decided to take a look to your channel, and this video was exactly what I needed for my algebra course, hoping to see diagonalization soon
@@TomRocksMaths Aha!! Love the shoutout to Grant!! I was hoping to get your thoughts on geometrical notions of EV's!! But regardless in recent times, I definitely watch 3Blue1Brown along with your videos to get a complete overview of the topics!! Recently, I have started watching Dr.Steve Brunton's (Associate Professor, University of Washington) channel too!! Afterall, the more insights that I get... the more I appreciate the lore behind the math!!
I was practicing elementary row ops for the 3x3 example, so I did r3 + r2/lambda. You end up getting an extraneous soln of 0. Btw how do you work backwards to get the A matrix from a given Eigenvalue and Eigenvector? Eg, lambda = 2, and (1, 0, 0) like the example. Or are these vectors sort of just for some characteristic of the matrix that is useful to us?
Brilliant. But couldn't we just argue that the determinant of a transformation matrix represents the scale factor applied to the modulus of a vector? So if we want a result of zero when applied to a non-zero vector, we need a determinant of zero?
ok there's one thing I'm slightly confused by. Where does the 6-landa come from? in my head that became 5 landa instead of 6 (I know this video came out one year ago but I'll shoot my shot.) I know this is a very simple thing to understand but I still don't really get it so yeah if anyone sees this and can explain it, it would be greatly appreciated 🙏
9:10 there’s a shortcut here where you can just put, where lambda = m, m^2 - (sum diagonal)m + detA which instantly gives the characteristic equation. I’m this case sum diagonal = 6, detA = 8. 10:06 better to complete the square.
unfortunately, this simply goes through the simple mechanics of determining values - zero explanation, insight, into what these represent. Frankly, could have gotten a smart 14 year old to do this video. You need to up your game mate, stop appealing to middle of the road engineering students.
