The Inverse and the Transpose

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Previous: 'Reflection Vectors'

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0:46Recap our current situation

0:46Recap our current situation

0:46Recap our current situation

1:45Start thinking about how we'll transform Normals

1:45Start thinking about how we'll transform Normals

1:45Start thinking about how we'll transform Normals

3:51Blackboard: Rotating Normals (is pretty straightforward)

3:51Blackboard: Rotating Normals (is pretty straightforward)

3:51Blackboard: Rotating Normals (is pretty straightforward)

5:01Blackboard: Non-uniform scaling gets a little bit hairy

5:01Blackboard: Non-uniform scaling gets a little bit hairy

5:01Blackboard: Non-uniform scaling gets a little bit hairy

6:17Blackboard: Pretending we have the edge of a gem

6:17Blackboard: Pretending we have the edge of a gem

6:17Blackboard: Pretending we have the edge of a gem

8:41Blackboard: Vectors are not all the same

8:41Blackboard: Vectors are not all the same

8:41Blackboard: Vectors are not all the same

11:23Blackboard: Normals are written differently in linear algebra

11:23Blackboard: Normals are written differently in linear algebra

11:23Blackboard: Normals are written differently in linear algebra

12:46Blackboard: Sometimes you have to go down a math hole^{α}

12:46Blackboard: Sometimes you have to go down a math hole^{α}

12:46Blackboard: Sometimes you have to go down a math hole^{α}

13:03Blackboard: Constructing the P vectors

13:03Blackboard: Constructing the P vectors

13:03Blackboard: Constructing the P vectors

14:17Blackboard: Matrix multiplication

14:17Blackboard: Matrix multiplication

14:17Blackboard: Matrix multiplication

24:18Blackboard: Transpose operation

24:18Blackboard: Transpose operation

24:18Blackboard: Transpose operation

26:19Blackboard: Inverse operation

26:19Blackboard: Inverse operation

26:19Blackboard: Inverse operation

30:24Blackboard: Gauss steps in with Gaussian Elimination

30:24Blackboard: Gauss steps in with Gaussian Elimination

30:24Blackboard: Gauss steps in with Gaussian Elimination

35:26Blackboard: Solving equations in multiple unknowns

35:26Blackboard: Solving equations in multiple unknowns

35:26Blackboard: Solving equations in multiple unknowns

36:33Blackboard: We're just entirely in the math hole^{β}

36:33Blackboard: We're just entirely in the math hole^{β}

36:33Blackboard: We're just entirely in the math hole^{β}

37:17Blackboard: You can add or multiply any two equations with equal terms for free

37:17Blackboard: You can add or multiply any two equations with equal terms for free

37:17Blackboard: You can add or multiply any two equations with equal terms for free

39:02Blackboard: We can regularise operations on the rows and columns of this matrix

39:02Blackboard: We can regularise operations on the rows and columns of this matrix

39:02Blackboard: We can regularise operations on the rows and columns of this matrix

39:49Blackboard: Use numbers to clearly demonstrate Gaussian Elimination

39:49Blackboard: Use numbers to clearly demonstrate Gaussian Elimination

39:49Blackboard: Use numbers to clearly demonstrate Gaussian Elimination

41:12Blackboard: This is not JZ's term^{γ}

41:12Blackboard: This is not JZ's term^{γ}

41:12Blackboard: This is not JZ's term^{γ}

41:27Blackboard: You can then divide the last remaining term by whatever the target is

41:27Blackboard: You can then divide the last remaining term by whatever the target is

41:27Blackboard: You can then divide the last remaining term by whatever the target is

43:10Blackboard: We want to be able to multiply a matrix by something in order to produce that identity matrix

43:10Blackboard: We want to be able to multiply a matrix by something in order to produce that identity matrix

44:38Blackboard: The regular solution form for Gaussian Elimination

44:38Blackboard: The regular solution form for Gaussian Elimination

44:38Blackboard: The regular solution form for Gaussian Elimination

58:12Blackboard: Unfortunately we didn't quite get to the inverse transpose

58:12Blackboard: Unfortunately we didn't quite get to the inverse transpose

58:12Blackboard: Unfortunately we didn't quite get to the inverse transpose

1:02:26Q&A^{δ}

1:02:26Q&A^{δ}

1:02:26Q&A^{δ}

1:26:46Blackboard: Look at all of this maths

1:26:46Blackboard: Look at all of this maths

1:26:46Blackboard: Look at all of this maths

1:27:30Blackboard: Setup for Day 102 and sign off

1:27:30Blackboard: Setup for Day 102 and sign off

1:27:30Blackboard: Setup for Day 102 and sign off

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Next: 'Transforming Normals Properly'

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