matrix_decomp

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

No annotations are provided, so the description carries the full behavioral burden, and it discloses almost nothing. It does not say that operations return wildly different shapes (trace/rank return scalars, transpose returns a matrix, LU returns factor matrices), nor what happens with non-square or singular input, nor whether errors are raised.

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 front-loaded sentence with no filler; the operation list is presented immediately after the purpose. It is efficient, though the fragmentary 'decomposition and analysis' clause is slightly redundant padding.

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 no output schema and four operations that return fundamentally different result types (scalar for trace, integer for rank, matrix for transpose, paired matrices for LU), the description leaves the agent unable to predict the response shape or how to interpret results. For a multi-mode math tool this is a meaningful omission.

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 the schema already documents both parameters including the operation list and the 'lu' default. The description merely repeats the operation names without adding syntax, constraints, or format details, so baseline 3 applies.

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 gives a specific resource (matrix) and enumerates the four concrete operations (LU factorization, transpose, trace, rank), so an agent knows exactly what it does. It loses a point for not distinguishing itself from close siblings like matrix_rank (which overlaps the 'rank' operation) or matrix_operate.

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 when-to-use guidance, no prerequisites, and no naming of alternatives. An agent cannot tell from this text why it should call matrix_decomp for rank instead of the dedicated matrix_rank sibling, or how it relates to matrix_inverse for LU-related work.

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