Matrix Addition & Subtraction Calculator
Add or subtract matrices of the same dimensions.
Select Operation
Select Matrix Size
How Matrix Addition & Subtraction Works
Matrix addition and subtraction are performed element-wise:
For matrices A and B of the same dimensions:
Addition: \[ (A + B)_{ij} = A_{ij} + B_{ij} \]
Subtraction: \[ (A - B)_{ij} = A_{ij} - B_{ij} \]
Properties:
- Commutative: A + B = B + A
- Associative: (A + B) + C = A + (B + C)
- Additive Identity: A + 0 = A
- Additive Inverse: A + (-A) = 0
Example:
For 2×2 matrices:
\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \pm \begin{pmatrix} e & f \\ g & h \end{pmatrix} = \begin{pmatrix} a \pm e & b \pm f \\ c \pm g & d \pm h \end{pmatrix} \]
Applications:
- Linear transformations
- Image processing
- Computer graphics
- Quantum mechanics
- Economics and finance