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CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Change of Basis Calculator

Build the exact transition matrix between two ordered bases.

Linear Algebra & Matrices

Enter matrix values

Exact structural results; labelled numerical approximations where required

From-basis matrix

RowsColumns

From-basis matrix, row 1, column 1From-basis matrix, row 1, column 2From-basis matrix, row 2, column 1From-basis matrix, row 2, column 2

To-basis matrix

RowsColumns

To-basis matrix, row 1, column 1To-basis matrix, row 1, column 2To-basis matrix, row 2, column 1To-basis matrix, row 2, column 2

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.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

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

Calculation method

Apply the stated linear-algebra contract

C[to←from] = B_to⁻¹B_from

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

Worked example

Example interpretation

Multiplying by this matrix converts from-basis coordinates into to-basis coordinates.

C[to←from] = B_to⁻¹B_from

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.