CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Jordan Normal Form Calculator

Find a deliberately restricted real 2 × 2 Jordan form.

Linear Algebra & Matrices

Enter matrix values

Exact structural results; labelled numerical approximations where required
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Matrix A

Use signed finite decimals. Fill every visible cell. Fractions, commas, and scientific notation are not accepted.

Linear algebra result

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Understand the subject

What is Jordan normal form?

Jordan form describes a matrix that lacks enough eigenvectors by using blocks that retain the repeated-eigenvalue linkage.

Use it only for the deliberately restricted real two-by-two cases supported here.

The relationship

The defining relationship

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

A≈PJP⁻¹

Interpret with care

Important boundary

Complex eigenvalues and larger matrices are intentionally outside this calculator’s contract.

Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.

Extended domain

Complex 2 × 2 Jordan analysis

Repeated eigenvalues are separated into scalar or defective cases; distinct complex eigenvalues form diagonal Jordan blocks.

Try an example
EIGENVALUESr1 = 2r2 = 2

Defective case: one 2 × 2 Jordan block.

ReImr1r2

Quick guide

How to use this calculator

  1. Set the matrix dimensions required by the task.
  2. Fill every visible entry and any operation-specific control.
  3. Read the result type, factors, classification, and disclosed limitations.

Calculation method

Apply the stated linear-algebra contract

A ≈ PJP⁻¹

Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.

Worked example

Example interpretation

A defective repeated eigenvalue produces one 2 × 2 Jordan block.

A ≈ PJP⁻¹

Supported inputs

Precision and limits

Matrix size

Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.

Entry precision

Enter signed finite decimals with at most 30 digits and 15 decimal places.

Numerical policy

Results use real double-precision arithmetic, a 1e-10 structural tolerance where stated, bounded iterations, and labelled approximations.

Complex 2 × 2 extension

The established panel retains its exact or larger real-matrix workflow. The extended panel accepts complex entries for a bounded 2 × 2 analysis, reports both eigenvalues, and states branch or diagonalizability limitations.