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 .pi/skills/math-mode/SKILL.md for full tool documentation.