CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Matrix Addition Calculator

Add two equally sized matrices entry by entry with exact arithmetic.

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 addition do?

Addition combines entries occupying the same row and column.

Use it when two matrices describe compatible quantities on the same layout.

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

Both matrices must have exactly the same dimensions.

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 and copy the exact sum.

Calculation method

Add corresponding entries

If A and B have the same number of rows and columns, the entry in row i and column j of A + B is aᵢⱼ + bᵢⱼ.

Worked example

Add two 2 × 2 matrices

Add each entry of [[1,2],[3,4]] to the entry in the same position of [[5,6],[7,8]].

[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]

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.