Inverse and Transpose Matrices
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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
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
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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58:02stropheum 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
58:32A few words on how cool linear algebra can get
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?
🗪
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?
🗪
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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