CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Matrix Properties Calculator

Classify exact diagonal, triangular, symmetric, skew-symmetric, identity, zero, and orthogonal structure.

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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Enter valid values to see the result.

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Understand the subject

What are matrix properties?

Properties such as symmetric, triangular, diagonal, and orthogonal describe structural rules an entire matrix satisfies.

Use them to identify which theorems and factorizations may apply.

The relationship

The defining relationship

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

symmetric: Aᵀ=A; orthogonal: AᵀA=I

Interpret with care

Important boundary

A matrix may have several properties at once; passing one does not imply all others.

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

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

Symmetric: Aᵀ=A; orthogonal: AᵀA=I

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

Worked example

Example interpretation

The identity matrix is diagonal, triangular, symmetric, and orthogonal.

Symmetric: Aᵀ=A; orthogonal: AᵀA=I

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.

Exactness

Finite decimals become reduced rational numbers and intermediate structural calculations are not rounded.