Eigenvalue/Eigenvector Visualizer (2D) implementation

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

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