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$$ \Large \text{Build the vocabulary. Understand the relationships. Then use it.} $$

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<aside> âť—

Matrices from the ground up, with no assumptions and no unnecessary complexity. If a concept doesn’t immediately connect to something else, that’s okay. Focus on understanding that one idea and move on to the next. One more. Then one more. Eventually, you’ll look back and realize you understand the whole thing.

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Chapter 1 - Essential Vocabulary

What is a Matrix?

Creating Matrices

🍌 Identity Matrix - The equivalent of doing nothing.

Create Identity Matrix (Ident)

Determinant - is a number (one float) calculated from a matrix that tells us how the transformation affects space.

Calculate Determinant in VEX

Inverse of a Matrix

Invert Matrix and Create Identity Matrix in VEX

Transpose Matrix

Transpose in VEX

Chapter 2 - The Fundamental Operation

Multiplication

Multiplication with Scalar

Multiplication Matrix x Matrix

The commandments of Matrix Multiplication

Matrix Multiplication Explained

In VEX

Multiplication with Identity Matrix

Multiplication with Transposed Matrix

Multiplication with Vector

In Houdini: vectors go on the left.

Vector by 4x4 Matrix in Houdini/Vex

In Vex

Chapter 3 - About Translation and Scaling

Matrix Translation

Matrix translation

Matrix translation Math Step by Step

Matrix Translation In Vex

Vector Translation Comparison

Vector translation Math Step by Step

Vector Translation In Vex

Matrix Scaling

Matrix Scaling Math Step by Step

Matrix Scaling in Vex

Vector Scaling Comparison

Vector Scaling Math Step by Step

Vector Scaling In Vex

Chapter 4 - About Rotations

Matrix Rotation

Matrix Rotation

Matrix Rotation Math Step by Step & Why You Already Know It

Matrix Rotation In Vex

Vector Rotation Comparison

Vector Rotation Math Step by Step

Vector Rotation In Vex

Chapter 5 - Your Everyday Toolbox

Your Toolset in Houdini

Scale - Rotate - Translate

Make Transform

Crack Transform

Invert Transform

Dihedral

Look At

Instance

Chapter 6 - Conclusion