Finds the dominant eigenvalue and corresponding eigenvector of a square matrix, with configurable tolerance and maximum iterations.
Find the dominant eigenvalue and eigenvector of a square matrix via power iteration.
| Name | Required | Description | Default |
|---|---|---|---|
| matrix | Yes | Square NxN matrix | |
| tolerance | No | Convergence tolerance (default 1e-10) | |
| max_iterations | No | Max iterations (default 1000) |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full behavioral burden. It states the algorithm but omits convergence behavior, failure modes when no dominant eigenvalue exists, what happens if max_iterations is reached, and any assumptions about the matrix.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
A single sentence front-loads the operation and result without any filler. Every part of the sentence contributes to understanding the tool's core action.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a mathematical tool with no output schema, the description adequately states what is computed and how. However, it leaves out important assumptions and failure modes that an agent might need to use the tool correctly, so it is only minimally complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, and the schema already documents matrix, tolerance, and max_iterations clearly. The description adds no parameter-level meaning beyond what the schema provides, so the baseline of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description names a specific verb (Find), two precise resources (dominant eigenvalue and eigenvector), the input type (square matrix), and the method (power iteration). This is enough for an agent to distinguish it from generic matrix operations or decomposition tools.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
There is no guidance on when to prefer power iteration over other eigenvalue methods (e.g., matrix_decomp), nor any explicit conditions such as requiring a unique dominant eigenvalue or a suitable starting vector. Usage is only implied by the method name.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.