Source: https://guthlabs.ai/docs/instruments/eigenvalue-eigenvector-visualizer-2d/implementation/

instrument implementation / implementation-contract

# Eigenvalue/Eigenvector Visualizer (2D) implementation

A source-bound implementation contract for Eigenvalue/Eigenvector Visualizer (2D); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-125

**Effect**: Computation or source lookup only

## Input and validation requirements

The specification does not state how repeated eigenvalues with non-unique eigenspaces, zero-denominator solver cases, complex eigenvalues, or eigenvector sign and normalization conventions are handled. These inputs can cause incorrect directions, undefined arithmetic, or an invalid real plot unless explicitly guarded.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "matrix": [
      [
        2,
        0
      ],
      [
        0,
        3
      ]
    ],
    "sample_vectors": [
      [
        1,
        0
      ],
      [
        0,
        1
      ],
      [
        1,
        1
      ]
    ]
  },
  "expected_outputs": {
    "eigenvalues": [
      2,
      3
    ],
    "eigenvectors": {
      "lambda_2": [
        1,
        0
      ],
      "lambda_3": [
        0,
        1
      ]
    },
    "sampled_transformed_vectors": [
      {
        "input": [
          1,
          0
        ],
        "output": [
          2,
          0
        ]
      },
      {
        "input": [
          0,
          1
        ],
        "output": [
          0,
          3
        ]
      },
      {
        "input": [
          1,
          1
        ],
        "output": [
          2,
          3
        ]
      }
    ],
    "key_curve_features": [
      "Real invariant directions are the x-axis and y-axis.",
      "The origin is fixed.",
      "Vectors on the x-axis are stretched by factor 2; vectors on the y-axis are stretched by factor 3."
    ]
  },
  "working": "A-λI=[[2-λ,0],[0,3-λ]]. det(A-λI)=(2-λ)(3-λ)=0, so λ=2 or λ=3. For λ=2: [[0,0],[0,1]]v=0 gives y=0, so v=(1,0). For λ=3: [[-1,0],[0,0]]v=0 gives x=0, so v=(0,1). Direct products: A(1,0)=(2*1+0*0,0*1+3*0)=(2,0); A(0,1)=(0,3); A(1,1)=(2*1+0*1,0*1+3*1)=(2,3)."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/eigenvalue-eigenvector-visualizer-2d/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/eigenvalue-eigenvector-visualizer-2d/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/eigenvalue-eigenvector-visualizer-2d/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`