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

With no annotations provided, the description carries the full behavioral burden, and it does disclose something useful beyond the schema: the operation is pure CPU and instant, implying no network calls, no side effects, and no rate limits. It stops short of describing failure behavior (e.g., mismatched dimensions for add/multiply) or whether the result is returned as JSON rows, which leaves real gaps for an unannotated tool.

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?

Two short sentences with the operation list front-loaded and zero filler. It is efficient, though the trailing 'Pure CPU, instant' is a fragment that would read better attached to a fuller behavioral statement.

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 two-parameter pure-computation tool with full schema coverage, the essentials are present, but with no output schema the description should indicate the return shape (e.g., result as JSON rows) and should note that transpose only needs 'a'. Those omissions are minor but real for an unannotated tool.

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%, so both parameters are already documented as 'Matrix as JSON rows' and 'multiply, transpose or add.' The description merely restates those same three operation names and adds no syntax, dimension, or shape guidance beyond what the schema supplies, making the baseline 3 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 three concrete operations (multiply, transpose, add) applied to a specific resource (matrices), which is far more informative than the bare tool name 'matrix'. It does not, however, distinguish itself from near-neighbors in the sibling list such as math_eval or evaluate_math, so an agent must infer that this is the matrix-specific path.

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 like math_eval, evaluate_math, or geometry, and no prerequisites or exclusions. The only contextual remark, 'Pure CPU, instant,' describes cost rather than the conditions that should select this tool.

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