Matrix Calculator - Perform Matrix Operations Online
Use our comprehensive matrix calculator to perform various matrix operations including addition, subtraction, multiplication, determinant calculation, matrix inverse, transpose, and more. Perfect for linear algebra students, engineers, and anyone working with matrix mathematics.
Key Features
- Multiple Operations: Addition, subtraction, multiplication, determinant, inverse, transpose
- Flexible Matrix Sizes: Support for matrices up to 6×6
- Real-time Properties: View matrix properties like determinant, trace, and rank
- Step-by-Step Results: Clear display of calculation results
- Quick Presets: Identity matrix, zero matrix, and example values
- Error Validation: Checks for valid operations and matrix compatibility
Supported Matrix Operations
- Matrix Addition: Add two matrices of the same dimensions
- Matrix Subtraction: Subtract one matrix from another
- Matrix Multiplication: Multiply matrices (A×B where A columns = B rows)
- Determinant: Calculate the determinant of square matrices
- Matrix Transpose: Flip rows and columns of a matrix
- Matrix Inverse: Find the multiplicative inverse of square matrices
- Matrix Power: Raise a square matrix to a given power
- Trace: Sum of diagonal elements in square matrices
- Rank: Determine the rank of a matrix
How to Use the Matrix Calculator
- Select Operation: Choose the matrix operation you want to perform
- Set Dimensions: Enter the number of rows and columns for your matrices
- Enter Values: Fill in the matrix elements with your numbers
- Calculate: Click the calculate button to see results
- Review Properties: Check matrix properties and operation guidelines
Matrix Operation Rules
- Addition & Subtraction: Matrices must have identical dimensions (same rows and columns)
- Multiplication: The number of columns in the first matrix must equal the number of rows in the second matrix
- Determinant & Inverse: Only applicable to square matrices (same number of rows and columns)
- Inverse Existence: A matrix has an inverse only if its determinant is non-zero
- Transpose: Can be applied to any matrix, resulting in dimensions flipped
Applications of Matrix Calculations
- Linear Algebra: Solving systems of linear equations
- Computer Graphics: 3D transformations and rotations
- Engineering: Structural analysis and control systems
- Economics: Input-output models and optimization
- Statistics: Covariance matrices and data analysis
- Physics: Quantum mechanics and field theories
Common Matrix Types
- Identity Matrix: Square matrix with 1s on the diagonal and 0s elsewhere
- Zero Matrix: Matrix with all elements equal to zero
- Diagonal Matrix: Square matrix with non-zero elements only on the main diagonal
- Symmetric Matrix: Square matrix that is equal to its transpose
- Orthogonal Matrix: Square matrix whose columns and rows are orthogonal unit vectors
Tips for Matrix Calculations
- Check Dimensions: Always verify matrix dimensions before performing operations
- Determinant Zero: If determinant is zero, the matrix is singular and has no inverse
- Order Matters: Matrix multiplication is not commutative (A×B ≠ B×A)
- Precision: Be aware of floating-point precision in decimal calculations
- Verify Results: Cross-check important calculations using matrix properties
Frequently Asked Questions
- What is the maximum matrix size supported?
This calculator supports matrices up to 6×6 for optimal performance and readability. - Can I calculate the inverse of any square matrix?
Only square matrices with non-zero determinants have inverses. - What does "singular matrix" mean?
A singular matrix has a determinant of zero and cannot be inverted. - How is matrix multiplication different from element-wise multiplication?
Matrix multiplication follows specific rules where element (i,j) is the dot product of row i and column j.
Related Calculators
Determinant Calculator | Vector Calculator | Equation Solver | Basic Calculator