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Matrix Subtraction Calculator

Work out matrix subtraction instantly with clear inputs, formula shown and shareable results.

About Matrix Subtraction Calculator

Matrix subtraction works entry by entry, so both matrices must have identical dimensions. Unlike multiplication it is straightforward and commutes up to sign: A − B = −(B − A).

Formula

Matrix subtraction

(A − B)ᵢⱼ = Aᵢⱼ − Bᵢⱼ

Worked example

With the default values below, Matrix Subtraction Calculator returns A − B of [4, 5] [-2, 5]. Change any input above and every figure here is recalculated in your browser.

Inputs used

Matrix A, row by row
5, 8, 2, 7
Matrix B, row by row
1, 3, 4, 2
Columns per rowaccepts 1–8
2

Results

A − B
[4, 5] [-2, 5]
A + B for comparison
[6, 11] [6, 9]
Largest entry of A − B
5.000000
Sum of all entries of A − B
12.000000

Step by step

  1. 1Values used
  2. 2Matrix subtraction
  3. 3A − B= [4, 5] [-2, 5]
  4. 4A + B for comparison= [6, 11] [6, 9]
  5. 5Largest entry of A − B= 5.000000
  6. 6Sum of all entries of A − B= 12.000000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

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

[[4, 5], [−2, 5]], each entry taken independently.

Can I subtract matrices of different shapes?

No. Entry-by-entry operations require the same number of rows and columns.

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