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

Annotations already carry readOnlyHint=true, idempotentHint=true, and destructiveHint=false, so the safety profile is covered. The description adds genuine value beyond annotations by disclosing the ValueError failure modes (matrix not found, decomposition fails) and the expected return format. No contradiction with the annotations exists.

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?

The definition is compact and front-loaded with the core purpose. The Args/Returns sections are somewhat redundant with the schema and output schema, but the Raises section adds unique value. It is efficient without being over-redundant, though the Args block could be trimmed.

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 the output schema present, return format need not be spelled out in prose, and annotations cover safety. The description covers purpose, algorithm, and failure modes for the single parameter. It is essentially complete for a simple read-only tool; only alternative-routing guidance is absent.

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's parameter description ('Name of the stored matrix whose column space to orthogonalize.') is actually richer than the description's own 'name (str): The name of the matrix.' Since the schema already documents the single parameter fully, the description adds no additional semantics, warranting the baseline of 3.

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 states a specific verb ('finds'), a precise target ('orthonormal basis for the column space of a stored matrix'), and the method ('using QR decomposition'). This clearly differentiates it from the sibling `qr_decompose` (returns the factor pair) and `change_basis` (changes to an arbitrary basis), even without reading their schemas.

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?

The purpose is clear and the algorithm hint implies the use case (you want an orthogonalized column-space basis). However, there is no explicit guidance on when to choose this over `qr_decompose` or `change_basis`, and no exclusions or alternative conditions are stated, so the agent must infer the selection criteria.

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