➕➖ Matrix Addition and Subtraction Calculator
Add or subtract two matrices element-wise
How to Use This Calculator
Select Dimensions
Choose rows and columns (both matrices must have same size).
Choose Operation
Select addition (A + B) or subtraction (A - B).
Enter Matrices
Input elements of matrices A and B.
View Result
See the element-wise sum or difference of the matrices.
Formula
(A ± B)ᵢⱼ = Aᵢⱼ ± Bᵢⱼ
Element-wise addition or subtraction
Addition:
(A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Subtraction:
(A - B)ᵢⱼ = Aᵢⱼ - Bᵢⱼ
Requirements:
Matrices A and B must have the same dimensions (m × n)
Properties:
- Commutative: A + B = B + A
- Associative: (A + B) + C = A + (B + C)
- A + 0 = A (0 is zero matrix)
- A + (-A) = 0
About Matrix Addition and Subtraction Calculator
The Matrix Addition and Subtraction Calculator performs element-wise addition or subtraction of two matrices. Each element in the result is the sum or difference of corresponding elements from the input matrices. This is one of the fundamental matrix operations in linear algebra.
When to Use This Calculator
- Linear Algebra: Basic matrix operations
- Vector Spaces: Combining matrices in vector spaces
- Transformations: Combining linear transformations
- Data Processing: Combining datasets element-wise
- Statistics: Computing differences or sums of data matrices
Why Use Our Calculator?
- ✅ Both Operations: Addition and subtraction in one tool
- ✅ Flexible Size: Supports various matrix dimensions
- ✅ Clear Display: Shows input matrices and result
- ✅ Educational: Helps understand matrix operations
- ✅ Accurate: Precise calculations
- ✅ Free: No registration required
Key Concepts
- Element-wise: Operations performed position by position
- Same Dimensions: Both matrices must be same size
- Zero Matrix: Identity element for addition
- Negative Matrix: -A has elements -Aᵢⱼ
- Commutative: A + B = B + A
Frequently Asked Questions
Can I add matrices of different sizes?
No, matrix addition/subtraction requires identical dimensions. Both matrices must have the same number of rows and columns.
Is matrix addition commutative?
Yes! A + B = B + A for any matrices A and B (of same size) because addition of numbers is commutative.
What is the identity element for addition?
The zero matrix (all elements are 0) is the identity: A + 0 = A for any matrix A.
How is this different from matrix multiplication?
Addition/subtraction is element-wise (simple arithmetic). Multiplication involves dot products of rows and columns, requiring compatible (not identical) dimensions and following different rules.