From ab451b3466b7f5151db9556fdf326934f86bd246 Mon Sep 17 00:00:00 2001
From: j-james
Date: Tue, 15 Nov 2022 00:24:05 -0800
Subject: Add my linear algebra library

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+# lalge (name tbd)
+
+A functional, dead simple linear algebra library written in Nim. Mostly for learning purposes.
+
+This is also serving as my finals review, haha.
+
+If you're looking for an actually robust linear algebra library for Nim, check out [Neo](https://github.com/andreaferretti/neo).
+
+## What's this language?
+
+Nim is a compiled whitespace-sensitive systems language with a strong type system and interesting memory management capabilities.
+
+It doesn't quite beat Python's usability or Rust's features, but I like it quite a lot, and think it's a good complement to other languages I use.
+
+Nim's [UFCS](https://en.wikipedia.org/wiki/Uniform_Function_Call_Syntax) (TL;DR: `a.add(b) == add(a, b)`) and operator overloading support is also a major draw for this type of project.
+
+## Architecture
+
+lalge uses Nim's `seqs` - dynamic arrays, equivalent to Rust's `Vec`, Go's `slice`, or Java's `ArrayList` - to implement matrices. This may have some performance overhead. On the other hand, it has the benefit of making the code much simpler.
+
+This also has the benefit of being able to declare matrices as such:
+```nim
+example: Matrix = @[
+  @[1, 0, 0],
+  @[0, 1, 0],
+  @[0, 0, 1],
+]
+```
+
+## Goals
+- [ ] Cover the basic operations associated with the MATH 221 / typical introductory linear algebra curriculum
+  - [x] Addition / Subtraction
+  - [x] (Scalar / Vector) Multiplication
+  - [x] Inverse
+  - [x] Transpose
+  - [ ] Eigenvalues / Eigenvectors
+  - [ ] everything that i am forgetting
+- [ ] Helpful characteristic functions
+  - [ ] Dimension
+  - [ ] Rank / Nullity
+  - [ ] Spans
+  - [ ] Determinant
+- [x] Support arbitrary-sized matrices with internal seq representation
+- [x] Support specialized "vectors", as opposed to Nx1 matrices
+
+After I get to a reasonable point of completeness, I'd love to go through and compare my library to Eigen (generally praised as a Very Good library)
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