The Inverse and the Transpose — Handmade Hero — Episode Guide

0:46Recap our current situation

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

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

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

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

8:41Blackboard: Vectors are not all the same

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

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

13:03Blackboard: Constructing the P vectors

14:17Blackboard: Matrix multiplication

24:18Blackboard: Transpose operation

26:19Blackboard: Inverse operation

30:24Blackboard: Gauss steps in with Gaussian Elimination

35:26Blackboard: Solving equations in multiple unknowns

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

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

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

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

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

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

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

1:02:26Q&A^δ

1:03:06stelar7 For inverting 2x2 matrices, a simple cofactor equation is quite efficient

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1:03:06stelar7 For inverting 2x2 matrices, a simple cofactor equation is quite efficient

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1:03:06stelar7 For inverting 2x2 matrices, a simple cofactor equation is quite efficient

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1:03:26mr4thdimention All of the steps in elimination can be represented as a matrix. Starting with M and multiply by all those matrices you get the identity. So those matrices multiplied together are the inverse. Multiplying them all by the identity gives you the inverse. Is that the trick you are alluding to?

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1:03:26mr4thdimention All of the steps in elimination can be represented as a matrix. Starting with M and multiply by all those matrices you get the identity. So those matrices multiplied together are the inverse. Multiplying them all by the identity gives you the inverse. Is that the trick you are alluding to?

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1:03:26mr4thdimention All of the steps in elimination can be represented as a matrix. Starting with M and multiply by all those matrices you get the identity. So those matrices multiplied together are the inverse. Multiplying them all by the identity gives you the inverse. Is that the trick you are alluding to?

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1:07:47robotchocolatedino To find the inverse matrix couldn't we just rotate by the negative angle and scale by 1 over the amount that we scaled by originally?

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1:07:47robotchocolatedino To find the inverse matrix couldn't we just rotate by the negative angle and scale by 1 over the amount that we scaled by originally?

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1:07:47robotchocolatedino To find the inverse matrix couldn't we just rotate by the negative angle and scale by 1 over the amount that we scaled by originally?

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1:17:32oliholli I remember doing this by putting the identity besides the original matrix and performing each step to each

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1:17:32oliholli I remember doing this by putting the identity besides the original matrix and performing each step to each

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1:17:32oliholli I remember doing this by putting the identity besides the original matrix and performing each step to each

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1:21:24ufphen If you had a matrix such as int[2][2] with the example of abcd as the variables in place, couldn't you just swap a and d and make c and b negative?

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1:21:24ufphen If you had a matrix such as int[2][2] with the example of abcd as the variables in place, couldn't you just swap a and d and make c and b negative?

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1:21:24ufphen If you had a matrix such as int[2][2] with the example of abcd as the variables in place, couldn't you just swap a and d and make c and b negative?

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1:22:31miblo I understood none of today's episode. Would you recommend that I rewatch it, or do you think all may become clear tomorrow?

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1:22:31miblo I understood none of today's episode. Would you recommend that I rewatch it, or do you think all may become clear tomorrow?

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1:22:31miblo I understood none of today's episode. Would you recommend that I rewatch it, or do you think all may become clear tomorrow?

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1:23:31naysayer88 If you write A and then I next to each other, and apply a bunch of operations, you are computing T3T2T1 A and T3T2T1 I. Because you ended up at the identity, T3T2T1A = I. So T3T2T1 = A^-1. Therefore T3T2T1 I = A^-1

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1:23:31naysayer88 If you write A and then I next to each other, and apply a bunch of operations, you are computing T3T2T1 A and T3T2T1 I. Because you ended up at the identity, T3T2T1A = I. So T3T2T1 = A^-1. Therefore T3T2T1 I = A^-1

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1:23:31naysayer88 If you write A and then I next to each other, and apply a bunch of operations, you are computing T3T2T1 A and T3T2T1 I. Because you ended up at the identity, T3T2T1A = I. So T3T2T1 = A^-1. Therefore T3T2T1 I = A^-1

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

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

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