CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Matrix Subtraction Calculator

Subtract one matrix from another entry by entry without rounding.

Linear Algebra & Matrices

Enter matrix values

Exact rational arithmetic
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Matrix A
Matrix B

Use ordinary signed decimals. Fractions, commas, and scientific notation are not accepted in this first batch.

Exact result

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Enter valid values to see the result.

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Understand the subject

What does matrix subtraction do?

Subtraction compares corresponding entries in the same ordered layout.

Use it to find an exact entry-by-entry change from B to A.

The relationship

The defining relationship

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

(A−B)ᵢⱼ = aᵢⱼ − bᵢⱼ

Interpret with care

Important boundary

Changing the order changes the sign of every difference.

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. Give A and B matching dimensions.
  2. Enter every matrix value.
  3. Read A − B in the original row and column order.

Calculation method

Subtract corresponding entries

For equally sized matrices, subtract each entry of B from the entry occupying the same position in A.

Worked example

Subtract two 2 × 2 matrices

Subtract [[1,2],[3,4]] from [[5,6],[7,8]].

[[5,6],[7,8]] − [[1,2],[3,4]] = [[4,4],[4,4]]

Supported inputs

Precision and limits

Matrix size

Each input matrix may contain 1–6 rows and 1–6 columns.

Entry precision

Each signed decimal may contain up to 30 digits and 15 decimal places.

Exactness

Finite decimals are converted to reduced fractions before calculation; matrix arithmetic is not rounded.