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Personally, I think the matrix powers method is more impressive. You're using the matrix as a state engine to get to whatever state you intend to reach. That ha
by mytochar 12y ago
Personally, I think the matrix powers method is more impressive. You're using the matrix as a state engine to get to whatever state you intend to reach. That has more applications than just the closed form, which a lot of people know about, and you most likely just happened to memorize.
Don't get me wrong, it'd still be impressive "Woah, he memorized this!" but seeing someone do the matrix trick would be even more impressive, to me.
- hacknat 12y agofair enough.
- fdej 12y agoThe closed form is just the diagonalized version of the matrix power, though.
- mytochar 12y agoI honestly didn't know that until it was mentioned in another part of this thread. My point was that someone can memorize the formula. Chances are, they'll see the matrix form and actually know how to use that in other situations. Now, if you derived the formula on the board from the matrix, that'd be incredibly impressive. The idea here is how the person's brain thinks. When I see them write an equation on the board, I think "Oh, they memorized it" when I see them step through the process of creating a matrix and doing matrix multiplication, I think "Wow, they /really/ know their stuff". If they just threw up the matrix and couldn't explain it, I wouldn't be as impressed. Same as if they wrote the equation and couldn't explain it. At the end of the day, if they could explain either approach, I'd be impressed, I think the matrix form just lends itself to more likely be in a way that the person can explain it