🔢 Matrix Calculator
Perform various matrix operations
How to Use This Calculator
Select Operation
Choose the matrix operation you want to perform.
Set Dimensions
Set matrix dimensions based on the operation.
Enter Matrices
Input matrix elements (or scalar for scalar multiplication).
Get Result
View the computed result.
Formulas
Various matrix operations available
See individual calculator pages for detailed formulas
Addition/Subtraction:
(A ± B)ᵢⱼ = Aᵢⱼ ± Bᵢⱼ
Multiplication:
(AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ
Transpose:
(Aᵀ)ᵢⱼ = Aⱼᵢ
Determinant:
det(A) = Σ (-1)^(i+j) aᵢⱼ det(Mᵢⱼ)
Trace:
tr(A) = Σᵢ Aᵢᵢ
About Matrix Calculator
The Matrix Calculator is a comprehensive tool for performing various matrix operations. It supports addition, subtraction, multiplication, scalar multiplication, transpose, determinant, and trace calculations all in one place.
Operations Supported
- Addition: Element-wise addition of two matrices
- Subtraction: Element-wise subtraction of two matrices
- Multiplication: Matrix multiplication (A × B)
- Scalar Multiplication: Multiply matrix by a number
- Transpose: Flip matrix across diagonal
- Determinant: Scalar representing matrix property
- Trace: Sum of diagonal elements
Why Use Our Calculator?
- ✅ All-in-One: Multiple operations in one tool
- ✅ Flexible: Works with various matrix sizes
- ✅ Clear Display: Easy to read results
- ✅ Educational: Helps learn matrix operations
- ✅ Accurate: Precise calculations
- ✅ Free: No registration required
Frequently Asked Questions
What's the difference between matrix addition and multiplication?
Addition is element-wise (A + B = [a₁₁+b₁₁ a₁₂+b₁₂ ...]). Multiplication uses dot products of rows and columns (each element is a sum of products). Addition requires same dimensions; multiplication requires compatible inner dimensions.
Can I do multiple operations in sequence?
Not directly - each calculation is separate. For complex operations like (A + B) × C, you'd need to compute A + B first, then multiply the result by C in a second step.
What if determinant or trace requires non-square matrix?
These operations only work for square matrices (same number of rows and columns). The calculator will show an error if you try to compute det or trace for a rectangular matrix.
Is there a way to compute matrix inverse here?
Not in this calculator, but you can find dedicated inverse matrix calculators in the Linear Algebra section. For A⁻¹, compute det(A) first to check if inverse exists (det ≠ 0).