# Linear Algebra

> Vector spaces and linear transformations

- Skill: `ffsshhttiikk/linear-algebra` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ffsshhttiikk/linear-algebra`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ffsshhttiikk/linear-algebra/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: ffsshhttiikk (https://skillmd.com/u/ffsshhttiikk)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ffsshhttiikk/linear-algebra

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## What I do
- Perform matrix operations and factorizations
- Solve systems of linear equations
- Find eigenvalues and eigenvectors
- Compute determinants and inverses
- Apply singular value decomposition
- Work with vector spaces and linear transformations

## When to use me
When solving linear systems, analyzing transformations, or performing dimensionality reduction.

## Key Concepts
- **Matrix Multiplication**: (AB)_{ij} = Σ_k A_{ik}B_{kj}, generally non-commutative
- **Determinant**: det(A) nonzero implies invertibility; det(AB) = det(A)det(B)
- **Eigenvalue Equation**: Av = λv, characteristic polynomial det(A - λI) = 0
- **LU Decomposition**: A = LU for solving Ax = b efficiently
- **SVD**: A = UΣV^T, reveals rank, pseudoinverse, and low-rank approximations
- **Rank**: Dimension of column/row space; rank(A) = n - nullity(A)