Home

Matrix Addition

Matrix addition and subtraction calculator. Enter same-size A and B to compute A+B and A−B elementwise—for matrix basics.

展开更多 ▾
(A±B)ᵢⱼ = aᵢⱼ ± bᵢⱼ
space-separated entries, semicolon-separated rows, e.g. 1 2;3 4
space-separated entries, semicolon-separated rows, e.g. 1 2;3 4

📖 Tutorial｜Matrix Addition

1. Definition
Two same-size matrices (same rows and columns) are added entrywise to form A+B.
2. Symbols
SymbolMeaning
(A+B)ᵢⱼentry aᵢⱼ+bᵢⱼ
same-sizeequal rows and columns
3. How this tool works
  • Only same-size matrices can be added;
  • Addition is entrywise, not across rows or columns;
  • A−B = A+(−B).
4. Steps
  1. Enter same-size A and B;
  2. Click Calculate to see A+B and A−B;
  3. Mismatched sizes raise an error.
5. Example
Example: A=1 2;3 4, B=5 6;7 8. A+B=6 8;10 12, A−B=−4 −4;−4 −4.
6. Pitfalls
Matrices of different sizes cannot be added;
Addition does not change the dimensions;
Watch signs when entries are negative.

❓ FAQ｜Matrix Addition

Can matrices of different sizes be added?
No; only same-size matrices with equal rows and columns.
Is matrix addition commutative?
Yes: A+B=B+A, and associative too.
How to compute A−B?
Subtract entrywise, i.e. A+(−B).
Does addition change the size?
No; the result has the same dimensions.
Input format?
Semicolons for rows, spaces for columns.