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

Annotations already declare readOnlyHint=true, destructiveHint=false and openWorldHint=false, so the safety profile is covered and the bar is lower. The description adds only the tolerance of complex inputs; it says nothing about behavior on non-square input or about numeric precision, which are the real risks for this operation.

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?

One compact sentence with no filler and the scope constraint front and center. It is efficient, though the terseness edges toward under-specification rather than pure economy.

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?

With an output schema present and only one required parameter, the description needn't explain return values, and annotations cover safety. Still, for a math operation that can fail on non-square input or produce complex results, the definition leaves the agent to infer error behavior entirely.

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 coverage is 100% and the single parameter already carries the description 'Square matrix.' plus an example, so the schema does the heavy lifting. The description's '(real or complex)' adds a small amount of accepted-domain information but does not explain nesting/ordering expectations beyond the example.

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 the resource (eigenvalues) and the input domain (square matrix, real or complex), so an agent can identify the computation. However it is a noun phrase with no verb and does not distinguish itself from the closely related sibling calculator_eigenvectors or from calculator_determinant, which share the same matrix input. Purpose is inferable but not crisply delimited.

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 statement of when to use this tool versus alternatives; the near-identical sibling calculator_eigenvectors is never mentioned, nor is any precondition beyond 'square matrix'. The agent must infer the selection rule from the tool name alone.

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