[video output=day319 member=cmuratori stream_platform=twitch stream_username=handmade_hero project=code title="Inverse and Transpose Matrices" vod_platform=youtube id=9KaIB7PFWeE annotator=Miblo]
[0:17][Recap and set the stage for the day]
[1:29][Blackboard: Skew UV Mapping]
[3:48][Blackboard: A conceptual explanation of transforming a texture map]
[7:15][Blackboard: Our matrix equation]
[8:08][Blackboard: The components of this equation]
[9:27][Blackboard: Adding and taking the origin out of equation]
[10:36][Blackboard: Transforming the U and V]
[12:11][Blackboard: Multiplying these matrices out]
[14:11][Blackboard: Backward transform, using dot products]
[16:18][Blackboard: Why use dot products to compute the transformed U and V?]
[18:42][Blackboard: Getting from wanting to invert the matrix, to taking the dot product shortcut]
[19:47][Blackboard: Inverting an orthonormal matrix]
[22:08][Blackboard: What it means to invert]
[25:14][Blackboard: The algebraic explanation for why any orthonormal matrix multiplied by its transpose (i.e. inverted) gives you the identity matrix]
[31:38][Blackboard: Putting it in meta algebraic terms]
[33:22][Blackboard: The geometric explanation for this]
[37:28][Blackboard: Columnar vs Row-based Matrices]
[39:49][Blackboard: How non-uniform (yet still orthogonal) scaling affects our matrix]
[41:11]["I hope everyone was interested in the matrix thing today"][quote 516]
[42:16][Blackboard: Transposing the matrix for non-uniformly scaled vectors, and compensating for that scaling]
[44:54][Blackboard: The beginnings of a formal algebraic explanation of this compensation]
[46:53][Blackboard: Matrix multiplication is order dependent]
[50:01][Blackboard: How this order dependence of the transform is captured by matrix maths]
[52:41][Blackboard: A formal algebraic explanation for the scale and rotation compensation]
[55:59][Blackboard: A glimpse into the future of actually inverting the matrix]
[57:14][Q&A][:speech]
[58:02][@stropheum][You've got some salty dogs in your chat tonight, Casey]
[58:32][A few words on how cool linear algebra can get]
[59:46][@stropheum][Did you know you were going to have to implement the sort of reverse mapping when you took that shortcut before? Was it a deliberate choice or just a cut corner that had to be uncut?]
[1:00:35][@ttbjm][Is your elbow okay? Are you okay?]
[1:02:24][@lord_marshall_][Other than transpose, do you need much more from linear?]
[1:05:03][@lord_marshall_][We had one example from my linear algebra class in the book, that used computers. Was surprised to see it here]
[1:06:21][@rohit_n][sssmcgrath said this once, but math papers should be published with C source code]
[1:06:38][@jpmontielr][Have you seen Gilbert Strang's lectures on linear algebra?]
[1:07:40][@d3licious][You suggest students not knowing how to solve linear algebra problems by hand?]
[1:09:42][@jessem3y3r][Would you consider using C++ templates for matrices, say in 3D programming?]
[1:10:57][We are done][:speech]
[/video]
