/matrices

name: matrices
description: "Problem-solving strategies for matrices in linear algebra"
allowed-tools: [Bash, Read]

Matrices

When to Use

Use this skill when working on matrices problems in linear algebra.

Decision Tree

1. **Identify Matrix Type**

• Square, symmetric, orthogonal, diagonal?
• Check properties with `sympy_compute.py matrix_type`

2. **Basic Operations**

• Multiplication: `sympy_compute.py matmul "A" "B"`
• Inverse: `sympy_compute.py inverse "A"`
• Transpose: `sympy_compute.py transpose "A"`

3. **Solve Linear Systems**

• Ax = b: `sympy_compute.py linsolve "A" "b"`
• Check consistency with `z3_solve.py sat`

4. **Decompositions**

• LU: `sympy_compute.py lu "A"`
• QR: `sympy_compute.py qr "A"`
• SVD: `sympy_compute.py svd "A"`

Tool Commands

Sympy_Inverse

uv run python -m runtime.harness scripts/sympy_compute.py inverse "[[1,2],[3,4]]"

Sympy_Det

uv run python -m runtime.harness scripts/sympy_compute.py det "[[a,b],[c,d]]"

Sympy_Linsolve

uv run python -m runtime.harness scripts/sympy_compute.py linsolve "[[1,2],[3,4]]" "[5,6]"

Cognitive Tools Reference

See `.claude/skills/math-mode/SKILL.md` for full tool documentation.