# ubaidalam01/essence-of-linear-algebra- architecture

> Architecture diagram of the GitHub repository ubaidalam01/essence-of-linear-algebra-, generated by GitDiagram from its file tree, README and a sample of source files (last updated 2026-09-30). It is an AI-made overview: check details against the source.

- Interactive diagram: https://gitdiagram.com/ubaidalam01/essence-of-linear-algebra-
- Repository: https://github.com/ubaidalam01/essence-of-linear-algebra-

## Overview

This repository is a set of standalone Python lecture demonstrations for learning linear algebra, not a shared application or library. A learner runs a lecture script to see numerical examples, printed checks, and—where included—plots. The available excerpts show concepts ranging from vectors and transformations to eigenvalues and abstract vector spaces; scripts do not import one another. Other lecture files are listed in the source index but their contents were not sampled, so their topics and internal relationships are not inferred.

Main entry points: [`linear1.py`](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear1.py) (Lecture 1), [`linear2.py`](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear2.py) (Basis & Span), [`linear10.py`](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear10.py) (Cross Products), [`linear11.py`](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear11.py) (Cross Product Duality)

## Diagram (Mermaid)

```mermaid
flowchart TD

subgraph group_foundations["Vectors & Geometry"]
  node_linear1["Lecture 1<br/>[linear1.py]"]
  node_basis["Basis &amp; Span<br/>[linear2.py]"]
  node_cross["Cross Products<br/>[linear10.py]"]
  node_cross_duality["Cross Product Duality<br/>[linear11.py]"]
  node_vector_spaces["Abstract Vector Spaces<br/>[linear16.py]"]
end

subgraph group_transformations["Linear Transformations"]
  node_transform2d["2D Transform<br/>[linear3.py]"]
  node_composition["Transform Composition<br/>[linear4.py]"]
  node_transform3d["3D Transform<br/>[linear5.py]"]
  node_determinants["Determinants<br/>[linear6.py]"]
  node_linear7["Lecture 7<br/>[linear7.py]"]
  node_linear8["Lecture 8<br/>[linear8.py]"]
  node_linear9["Lecture 9<br/>[linear9.py]"]
  node_change_basis["Change of Basis<br/>[linear13.py]"]
end

subgraph group_systems["Linear Systems"]
  node_cramers["Cramer's Rule<br/>[linear12.py]"]
end

subgraph group_eigen["Eigen Analysis"]
  node_eigenvectors["Eigenvectors &amp; Values<br/>[linear14.py]"]
  node_eigen_trick["Eigenvalue Shortcut<br/>[linear15.py]"]
end

node_learner(("Learner"))

node_learner -->|"runs"| node_linear1
node_learner -->|"runs"| node_basis
node_learner -->|"runs"| node_cross
node_learner -->|"runs"| node_cross_duality
node_learner -->|"runs"| node_transform2d
node_learner -->|"runs"| node_composition
node_learner -->|"runs"| node_transform3d
node_learner -->|"runs"| node_determinants
node_learner -->|"runs"| node_linear7
node_learner -->|"runs"| node_linear8
node_learner -->|"runs"| node_linear9
node_learner -->|"runs"| node_cramers
node_learner -->|"runs"| node_change_basis
node_learner -->|"runs"| node_eigenvectors
node_learner -->|"runs"| node_eigen_trick
node_learner -->|"runs"| node_vector_spaces

click node_linear1 "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear1.py"
click node_basis "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear2.py"
click node_cross "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear10.py"
click node_cross_duality "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear11.py"
click node_transform2d "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear3.py"
click node_composition "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear4.py"
click node_transform3d "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear5.py"
click node_determinants "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear6.py"
click node_linear7 "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear7.py"
click node_linear8 "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear8.py"
click node_linear9 "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear9.py"
click node_cramers "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear12.py"
click node_change_basis "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear13.py"
click node_eigenvectors "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear14.py"
click node_eigen_trick "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear15.py"
click node_vector_spaces "https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear16.py"

classDef toneNeutral fill:#f8fafc,stroke:#334155,stroke-width:1.5px,color:#0f172a
classDef toneBlue fill:#dbeafe,stroke:#2563eb,stroke-width:1.5px,color:#172554
classDef toneAmber fill:#fef3c7,stroke:#d97706,stroke-width:1.5px,color:#78350f
classDef toneMint fill:#dcfce7,stroke:#16a34a,stroke-width:1.5px,color:#14532d
classDef toneRose fill:#ffe4e6,stroke:#e11d48,stroke-width:1.5px,color:#881337
classDef toneIndigo fill:#e0e7ff,stroke:#4f46e5,stroke-width:1.5px,color:#312e81
classDef toneTeal fill:#ccfbf1,stroke:#0f766e,stroke-width:1.5px,color:#134e4a
class node_linear1,node_basis,node_cross,node_cross_duality,node_vector_spaces toneBlue
class node_transform2d,node_composition,node_transform3d,node_determinants,node_linear7,node_linear8,node_linear9,node_change_basis toneAmber
class node_cramers toneMint
class node_eigenvectors,node_eigen_trick toneRose
class node_learner toneIndigo
```

## Components

### Vectors & Geometry

- [Lecture 1](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear1.py): `linear1.py`
- [Basis & Span](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear2.py): `linear2.py`
- [Cross Products](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear10.py): `linear10.py`
- [Cross Product Duality](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear11.py): `linear11.py`
- [Abstract Vector Spaces](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear16.py): `linear16.py`

### Linear Transformations

- [2D Transform](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear3.py): `linear3.py`
- [Transform Composition](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear4.py): `linear4.py`
- [3D Transform](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear5.py): `linear5.py`
- [Determinants](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear6.py): `linear6.py`
- [Lecture 7](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear7.py): `linear7.py`
- [Lecture 8](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear8.py): `linear8.py`
- [Lecture 9](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear9.py): `linear9.py`
- [Change of Basis](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear13.py): `linear13.py`

### Linear Systems

- [Cramer's Rule](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear12.py): `linear12.py`

### Eigen Analysis

- [Eigenvectors & Values](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear14.py): `linear14.py`
- [Eigenvalue Shortcut](https://github.com/ubaidalam01/essence-of-linear-algebra-/blob/main/linear15.py): `linear15.py`

### Other components

- **Learner**

## Connections

- Learner → Lecture 1: runs (evidence: `linear1.py`)
- Learner → Basis & Span: runs (evidence: `linear2.py`)
- Learner → Cross Products: runs (evidence: `linear10.py`)
- Learner → Cross Product Duality: runs (evidence: `linear11.py`)
- Learner → 2D Transform: runs (evidence: `linear3.py`)
- Learner → Transform Composition: runs (evidence: `linear4.py`)
- Learner → 3D Transform: runs (evidence: `linear5.py`)
- Learner → Determinants: runs (evidence: `linear6.py`)
- Learner → Lecture 7: runs
- Learner → Lecture 8: runs
- Learner → Lecture 9: runs
- Learner → Cramer's Rule: runs (evidence: `linear12.py`)
- Learner → Change of Basis: runs (evidence: `linear13.py`)
- Learner → Eigenvectors & Values: runs (evidence: `linear14.py`)
- Learner → Eigenvalue Shortcut: runs (evidence: `linear15.py`)
- Learner → Abstract Vector Spaces: runs (evidence: `linear16.py`)