Math MCP Learning

Matrix Eigenvalues

matrix_eigenvalues

Read-onlyIdempotent

Calculate the eigenvalues of a square matrix.

Input Schema

Name	Required	Description	Default
`matrix`	Yes	2D list of numbers representing a square matrix. Each inner list is a row. Example: [[4, 2], [1, 3]]

Output Schema

Name	Required	Description	Default
`size`	Yes
`error`	No
`topic`	Yes
`success`	Yes
`difficulty`	Yes
`eigenvalues`	No
`eigenvectors`	No
`complex_values`	No
`complex_eigenvalues_warning`	No

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedMar 30, 2026

addedInput schema / properties / matrix / description

Added value: +"2D list of numbers representing a square matrix. Each inner list is a row. Example: [[4, 2], [1, 3]]"

Changed2 schema fields changedMar 19, 2026

addedOutput schema / properties / complex_eigenvalues_warning

Added value: +{
+  "anyOf": [
+    {
+      "type": "string"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null
+}

addedOutput schema / properties / complex_values

Added value: +{
+  "anyOf": [
+    {
+      "items": {
+        "type": "string"
+      },
+      "type": "array"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null
+}

Changed4 schema fields changedFeb 21, 2026

removedOutput schema / additionalProperties
```
Removed value: -true
```

addedOutput schema / description

Added value: +"Result of matrix eigenvalues calculation."

addedOutput schema / properties

Added value: +{
+  "difficulty": {
+    "type": "string"
+  },
+  "eigenvalues": {
+    "anyOf": [
+      {
+        "items": {
+          "type": "number"
+        },
+        "type": "array"
+      },
+      {
+        "type": "null"
+      }
+    ],
+    "default": null
+  },
+  "eigenvectors": {
+    "anyOf": [
+      {
+        "items": {
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "type": "array"
+      },
+      {
+        "type": "null"
+      }
+    ],
+    "default": null
+  },
+  "error": {
+    "anyOf": [
+      {
+        "type": "string"
+      },
+      {
+        "type": "null"
+      }
+    ],
+    "default": null
+  },
+  "size": {
+    "type": "integer"
+  },
+  "success": {
+    "type": "boolean"
+  },
+  "topic": {
+    "type": "string"
+  }
+}

addedOutput schema / required

Added value: +[
+  "size",
+  "success",
+  "difficulty",
+  "topic"
+]

Changed2 schema fields changedFeb 19, 2026
- addedInput schema / additionalProperties
```
Added value: +false
```
- removedInput schema / properties / matrix / title
```
Removed value: -"Matrix"
```
Changed1 schema field changedFeb 14, 2026
- addedInput schema / properties / matrix / maxItems
```
Added value: +10000
```
First observedJan 31, 2026

TDQS

C2.9/5.0

Behavior2/5

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

Annotations already declare readOnlyHint and idempotentHint, covering the safety profile. The description adds nothing beyond that: no mention of whether complex eigenvalues are returned, behavior for non-symmetric or ill-conditioned matrices, or computational limits despite the 10000-item cap in the schema.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

A single tight sentence with no filler, front-loading the verb and resource. It is efficient, though the brevity edges toward under-specification for a numerical tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

An output schema exists, so return values need not be explained, and the single required parameter is fully documented in the schema. Still, edge-case behavior (non-square input handling, complex results, large-matrix performance) is absent for what is a nontrivial numerical operation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, with the 'square matrix' constraint, row layout, and an example already documented in the schema. The description's mention of 'square matrix' merely repeats the schema, so baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb (calculate) and resource (eigenvalues of a square matrix), so the operation is unmistakable. However, it offers no differentiation from closely named siblings like matrix_determinant or matrix_inverse, which an agent must disambiguate on its own.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

There is no guidance on when to use this versus matrix_determinant, matrix_inverse, or other matrix siblings, nor any note on preconditions such as squareness or numerical limitations. The agent is left to infer selection purely from the name.

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

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