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

No annotations are supplied, so the description carries the full behavioral burden, and it discloses nothing: not the return value (presumably a boolean), not error behavior for malformed input, not whether it validates or merely inspects. The text adds zero context beyond the name.

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?

Extremely short, but this is under-specification rather than conciseness, and the one line present is a verbatim duplicate of the name — the least informative possible sentence.

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?

A parameterized predicate tool with no annotations, no output schema, and undefined semantics for its two inputs. Nothing an agent needs in order to call it correctly is provided anywhere.

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 nominally 100%, but both descriptions are vacuous ('M to process', 'Matrix to process') and the two parameters appear redundant, with no indication of how 'm' differs from 'matrix' or what format either expects. The description does nothing to disambiguate them, so it falls below the baseline-3 case where a schema does the explaining.

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 is the tool name restated — 'Matrix Is Square: Matrix Is Square' — a pure tautology. It offers no verb+resource framing that would let an agent distinguish it from matrix-shape, matrix-rows, or matrix-cols, all of which also inspect matrix structure.

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?

No when-to-use, when-not-to-use, or alternative is mentioned. With ~20 sibling matrix tools nearby, the absence of any routing hint leaves the agent to guess from the identifier alone.

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