CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Linear Transformation Matrix Calculator

Apply a transformation matrix and interpret its standard-basis columns.

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
Input vector or vector matrix

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 does a transformation matrix do?

A matrix sends each input vector to an output vector linearly. Its columns are the images of standard basis directions.

Use it to apply, inspect, or construct a linear transformation.

The relationship

The defining relationship

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

T(v)=Av

Interpret with care

Important boundary

A matrix describes a transformation only relative to chosen input and output coordinate systems.

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

T(v) = Av

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

Worked example

Example interpretation

Column j of A is the image of the jth standard basis vector.

T(v) = Av

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.