Inverse and Transpose Matrices

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Previous: 'Optimizing Render Target Blends and Clears'

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0:17Recap and set the stage for the day

0:17Recap and set the stage for the day

0:17Recap and set the stage for the day

1:29Blackboard: Skew UV Mapping

1:29Blackboard: Skew UV Mapping

1:29Blackboard: Skew UV Mapping

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

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

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

7:15Blackboard: Our matrix equation

7:15Blackboard: Our matrix equation

7:15Blackboard: Our matrix equation

8:08Blackboard: The components of this equation

8:08Blackboard: The components of this equation

8:08Blackboard: The components of this equation

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

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

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

10:36Blackboard: Transforming the U and V

10:36Blackboard: Transforming the U and V

10:36Blackboard: Transforming the U and V

12:11Blackboard: Multiplying these matrices out

12:11Blackboard: Multiplying these matrices out

12:11Blackboard: Multiplying these matrices out

14:11Blackboard: Backward transform, using dot products

14:11Blackboard: Backward transform, using dot products

14:11Blackboard: Backward transform, using dot products

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

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

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

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

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

19:47Blackboard: Inverting an orthonormal matrix

19:47Blackboard: Inverting an orthonormal matrix

19:47Blackboard: Inverting an orthonormal matrix

22:08Blackboard: What it means to invert

22:08Blackboard: What it means to invert

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

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

31:38Blackboard: Putting it in meta algebraic terms

31:38Blackboard: Putting it in meta algebraic terms

33:22Blackboard: The geometric explanation for this

33:22Blackboard: The geometric explanation for this

33:22Blackboard: The geometric explanation for this

37:28Blackboard: Columnar vs Row-based Matrices

37:28Blackboard: Columnar vs Row-based Matrices

37:28Blackboard: Columnar vs Row-based Matrices

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

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

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

^{α}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

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

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

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

46:53Blackboard: Matrix multiplication is order dependent

46:53Blackboard: Matrix multiplication is order dependent

46:53Blackboard: Matrix multiplication is order dependent

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

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

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

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

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

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

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

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

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

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

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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Next: 'Inverting a 2x2 Matrix by Hand'

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