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[SQUEAKING] [RUSTLING] [CLICKING] ALAN EDELMAN: All right. Well, welcome to the second lecture for this IAP class on matrix calculus. Steven, do you want to say anything before I start on nonlinear versus linear maps? So Philip's going to help out right away. So here's a picture of Philip, the corgi. He's right over there, in case you haven't seen him yet. And you folks could actually grab your favorite photo. You don't have to use a corgi. You could have any photo you like. So here in Julia I'm just uploading this picture of Philip. And I've got a few different transformations of a corgi. And the reason why I'm showing this to you, it's because it's come to my attention that not everybody has a fairly good visual intuition as to the difference between a linear and a nonlinear map, or even a map. Here, so let's go ahead. Let me just ask a real quick simple question for starters. So here I'm just rotating. Right? So I'm r...

[SQUEAKING] [RUSTLING] [CLICKING] ALAN EDELMAN: So welcome, everybody, to this IAP class on matrix calculus. I'm Professor Alan Edelman. And the other professor is Steven Johnson, who's going to have-- he had to go out of town. And so we're going to take advantage of Zoom technology so that he could give lectures remotely. We did some testing of the audio and the video. So hopefully it'll work out just fine. So maybe just a quick introduction. So-- oh, good, good. Yes, Steven-- recording? STEVEN JOHNSON: I already started it. ALAN EDELMAN: All right. Thank you for the reminder. Yeah. So I even put the two reminders on the blackboard. Yeah, so that was reminder number one. Good. OK. So let's see. So both of us are in the math department. I'm also in CSAIL. And I run the Julia lab over in CSAIL. And my own research involves both mathematics as well as computing software. Steven, do you want to say a few words quickly about yourself? STEVEN JOHNSON: H...