https://github.com/rb-thompson/interdimensional-math

Math for machine learning.
https://github.com/rb-thompson/interdimensional-math

calculus linear-algebra multivariable-calculus probability-theory python

Last synced: 2 months ago
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Math for machine learning.

• Host: GitHub
• URL: https://github.com/rb-thompson/interdimensional-math
• Owner: rb-thompson
• Created: 2025-02-13T14:43:48.000Z (3 months ago)
• Default Branch: main
• Last Pushed: 2025-02-13T16:34:38.000Z (3 months ago)
• Last Synced: 2025-02-13T16:36:15.007Z (3 months ago)
• Topics: calculus, linear-algebra, multivariable-calculus, probability-theory, python
• Language: Python
• Homepage:
• Size: 2.93 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Interdimensional Math 

- [x] Linear Algebra

- [ ] Calculus

- [ ] Multivariable Calculus

- [ ] Probability Theory

## Fundamentals of Linear Algebra

> "Linear algebra’s the backbone of all the cool crap in computer science—graphics, machine learning, simulations, all that jazz."

1. Vectors: **The Building Blocks of Everything**

    - **In Computer Science**: Vectors are used for positions, velocities, colors(RGB), and more. In graphics, they're your 3d models. In machine learning, they're your data points. Don't forget it.

    - **Operations**:

        - **Addition**: Add two vectors 

        `(1,2) + (3,4) = (4,6)`

        - **Scalar Multiplication**: Multiply a vector by a number 

        `2 * (1,2) = (2,4)`

        - **Dot Product**: For (1,2) and (3,4), it's 

        `a * b = (1 * 3) + (2 * 4)`

2. Matrices: **Vectors on Steroids**

    - Matrices are just grids of numbers. Think of a bunch of vectors stacked together. A 2x3 matrix? That's 2 rows, 3 columns.

    - **In Computer Science**: Matrices are used for transformations in graphics (scaling, rotating, translating), neural networks (weights), and more.

    - **Operations**:

        - **Addition**: Same size matrices. Add them element by element. `(1,2;3,4) + (5,6;7,8) = (6,8;10,12)`

        - **Multiplication**: To multiply two matrices, the number of columns in the first has to match the number of rows in the second. 

        ```

        [1 2 3]   [7 8]      [1*7 + 2*9 + 3*11  1*8 + 2*10 + 3*12]

        [4 5 6] x [9 10]  =  [4*7 + 5*9 + 6*11  4*8 + 5*10 + 6*12]

                  [11 12]

        ```

    - **Transpose**: Flip the rows and columns. `(1,2:3,4)` becomes `(1,3; 2;4)`

    - **Identity Matrix**: A square matrix with 1s on the diagonal, 0s everywhere else. Magic, right? No, it's math.

3. Linear Transformations: **Bending Reality**

    - Matrices aren't *just* numbers. They're transformations. Multiply a vector by a matrice, and you're stretching, rotating, or squishing space.

    - **Examples**:

        - **Scaling**: Multiply by a diagonal matrix, like `(2,0;0,2)`, to double the size.

        - **Rotation**: Use a rotation matrix. For 90 degrees in 2D, it's `(0,-1;1,0)`.

        - **Translation**: In 3D graphics, use homogeneous coordinates. Add an extra 1 to your vector, like `(x,y,1)` and use a 3x3 matrix to move it around.

4. Determinants **and Inverses**: **The VIP of Matrices**

    - **Determinant**: Tells you if a matrix is invertible. For a 2x2 matrix `(a,b;c,d)`, it's `ad-bc`. If it's zero, the matrix is trash.

    - **Inverse**: The inverse matrix undoes what the original matrix did. If the determinant's zero, forget it--no inverse.

5. Eigenvectors and Eigenvalues: **The Secret Sauce**

    - The vectors that don't change direction when you transform them with a matrix. Shrinks and stretches (dimensionality reduction).

        - **Example**: For a matrix A, if A * v = λ * v, then v is an eigenvector, and λ is the eigenvalue. 

6. OK! Time to experiment with linear algebra and python. 

    - **Project: 2D Portal Simulator**:

        - We have got the basics. Now, let's build something cool--a 2D portal simulation. 

        - Let's use vectors for positions, matrices for transformations, and NumPy because we aren't doing this by hand. 

        - Goal: Simulate a portal that rotates and scales objects passing through it.

        **Step 1**: Run this in your terminal:

        ```bash

        pip install numpy

        ```

        > Know your tools → [NumPy: The Absolute Basics](https://numpy.org/doc/2.2/user/absolute_beginners.html)

        **Step 2**: Write the script. Simulate objects passing through a portal that rotates and scales them. Don't break space-time!

        **Step 3**: Plot the results. Play with the numbers. 

        

        ![plot](ips-plot.png)

        

        **Step 4**: **(Optional)** Experiment with additional portal transformations in `enhanced_matrix.py`.

        ![plot2](enhanced-ips-plot.png)