Inverse and Transpose Matrices — Handmade Hero — Episode Guide

0:17Recap and set the stage for the day

1:29Blackboard: Skew UV Mapping

3:48Blackboard: A conceptual explanation of transforming a texture map

7:15Blackboard: Our matrix equation

8:08Blackboard: The components of this equation

9:27Blackboard: Adding and taking the origin out of equation

10:36Blackboard: Transforming the U and V

12:11Blackboard: Multiplying these matrices out

14:11Blackboard: Backward transform, using dot products

16:18Blackboard: Why use dot products to compute the transformed U and V?

18:42Blackboard: Getting from wanting to invert the matrix, to taking the dot product shortcut

19:47Blackboard: Inverting an orthonormal matrix

22:08Blackboard: What it means to invert

25:14Blackboard: The algebraic explanation for why any orthonormal matrix multiplied by its transpose (i.e. inverted) gives you the identity matrix

31:38Blackboard: Putting it in meta algebraic terms

33:22Blackboard: The geometric explanation for this

37:28Blackboard: Columnar vs Row-based Matrices

39:49Blackboard: How non-uniform (yet still orthogonal) scaling affects our matrix

41:11"I hope everyone was interested in the matrix thing today"^α

42:16Blackboard: Transposing the matrix for non-uniformly scaled vectors, and compensating for that scaling

44:54Blackboard: The beginnings of a formal algebraic explanation of this compensation

46:53Blackboard: Matrix multiplication is order dependent

50:01Blackboard: How this order dependence of the transform is captured by matrix maths

52:41Blackboard: A formal algebraic explanation for the scale and rotation compensation

55:59Blackboard: A glimpse into the future of actually inverting the matrix

57:14Q&A

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57:14Q&A

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57:14Q&A

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58:02stropheum You've got some salty dogs in your chat tonight, Casey

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58:02stropheum You've got some salty dogs in your chat tonight, Casey

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58:02stropheum You've got some salty dogs in your chat tonight, Casey

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58:32A few words on how cool linear algebra can get

59:46stropheum 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?

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59:46stropheum 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?

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59:46stropheum 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?

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1:00:35ttbjm Is your elbow okay? Are you okay?

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1:00:35ttbjm Is your elbow okay? Are you okay?

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1:00:35ttbjm Is your elbow okay? Are you okay?

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1:02:24lord_marshall_ Other than transpose, do you need much more from linear?

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1:02:24lord_marshall_ Other than transpose, do you need much more from linear?

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1:02:24lord_marshall_ Other than transpose, do you need much more from linear?

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1:05:03lord_marshall_ We had one example from my linear algebra class in the book, that used computers. Was surprised to see it here

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1:05:03lord_marshall_ We had one example from my linear algebra class in the book, that used computers. Was surprised to see it here

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1:05:03lord_marshall_ We had one example from my linear algebra class in the book, that used computers. Was surprised to see it here

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1:06:21rohit_n sssmcgrath said this once, but math papers should be published with C source code

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1:06:21rohit_n sssmcgrath said this once, but math papers should be published with C source code

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1:06:21rohit_n sssmcgrath said this once, but math papers should be published with C source code

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1:06:38jpmontielr Have you seen Gilbert Strang's lectures on linear algebra?

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1:06:38jpmontielr Have you seen Gilbert Strang's lectures on linear algebra?

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1:06:38jpmontielr Have you seen Gilbert Strang's lectures on linear algebra?

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1:07:40d3licious You suggest students not knowing how to solve linear algebra problems by hand?

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1:07:40d3licious You suggest students not knowing how to solve linear algebra problems by hand?

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1:07:40d3licious You suggest students not knowing how to solve linear algebra problems by hand?

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1:09:42jessem3y3r Would you consider using C++ templates for matrices, say in 3D programming?

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1:09:42jessem3y3r Would you consider using C++ templates for matrices, say in 3D programming?

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1:09:42jessem3y3r Would you consider using C++ templates for matrices, say in 3D programming?

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1:10:57We are done

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1:10:57We are done

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1:10:57We are done

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