Symbolic Algebra MCP Server

matrix_eigenvectors

Calculates the eigenvectors of a stored matrix from its matrix key, returning an expression key for eigenvalue analysis and linear algebra workflows.

Instructions

Calculates the eigenvectors of a matrix using SymPy's eigenvects method.

Args:
    matrix_key: The key of the matrix to calculate eigenvectors for.

Example:
    # Create a matrix
    matrix_key = create_matrix([[1, 2], [2, 1]])

    # Calculate its eigenvectors
    evecs_key = matrix_eigenvectors(matrix_key)

Returns:
    A key for the eigenvectors expression (usually a list of tuples (eigenvalue, multiplicity, [eigenvectors])).

Input Schema

Name	Required	Description	Default
`matrix_key`	Yes

Output Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.1.0Oct 29, 2026

TDQS

A3.6/5.0

Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description must carry the behavioral burden. It discloses the method used and the return format (a key for the eigenvectors expression), which is useful. It does not state whether the operation is read-only or stateful, nor does it describe error conditions or constraints like square-matrix requirements.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The purpose is front-loaded in the first sentence, followed by structured Args, Example, and Returns sections. Each section adds value, though the example is somewhat verbose for a one-parameter tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the simple one-parameter schema, output schema availability, and lack of annotations, the description is largely complete: it explains what the tool does, how to supply the input key, and what the return key represents. Minor gaps remain around matrix constraints and state behavior.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It does: 'matrix_key: The key of the matrix to calculate eigenvectors for' adds clear meaning beyond the bare schema title, and the example demonstrates obtaining a key via create_matrix. It does not specify format details or square-matrix constraints, so not a 5.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific verb ('Calculates') and resource ('eigenvectors of a matrix') and names the underlying SymPy method. It is clearly distinct from matrix_eigenvalues by resource name, but does not explicitly say when to use this instead of eigenvalue calculation, so sibling differentiation is only implicit.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The example implies a workflow (create_matrix then matrix_eigenvectors), which provides some usage context. However, there is no explicit when-to-use guidance, no alternatives mentioned (e.g., matrix_eigenvalues), and no prerequisites such as the matrix being square.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.