Matrix Calculator
Calculate matrix operations: determinant, trace, and more.
Matrix Input
Matrix Result
Determinant
-2
Matrix Size:
2 × 2
About This Calculator
The Matrix Calculator performs various matrix operations including determinant, trace, and sum of elements. Matrices are rectangular arrays of numbers used in linear algebra, computer graphics, and many other fields.
This calculator supports basic matrix operations. Enter your matrix values and select the operation you want to perform. The calculator automatically updates results as you modify the matrix.
Note: This calculator supports matrices up to 3×3 for determinant calculation. For larger matrices or more operations, use specialized linear algebra software.
Formula & Calculation Method
Matrix Operations:
Determinant (2×2):
det(A) = a₁₁ × a₂₂ - a₁₂ × a₂₁
Determinant (3×3):
det(A) = a₁₁(a₂₂a₃₃ - a₂₃a₃₂) - a₁₂(a₂₁a₃₃ - a₂₃a₃₁) + a₁₃(a₂₁a₃₂ - a₂₂a₃₁)
Trace:
tr(A) = a₁₁ + a₂₂ + ... + aₙₙ
(sum of diagonal elements)
The determinant is a scalar value that can be computed from a square matrix. The trace is the sum of the diagonal elements of a square matrix. These operations are fundamental in linear algebra.
How to Use This Calculator
- Set Dimensions: Choose the number of rows and columns for your matrix.
- Enter Values: Input the matrix elements in the grid.
- Select Operation: Choose the operation (determinant, trace, or sum).
- View Result: See the calculated result automatically.
Frequently Asked Questions
What is a matrix?
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are used in linear algebra, computer graphics, statistics, and many other mathematical and scientific fields.
What is the determinant?
The determinant is a scalar value calculated from a square matrix. It provides information about the matrix, such as whether it is invertible (non-zero determinant) and the scaling factor of linear transformations.
What is the trace of a matrix?
The trace of a square matrix is the sum of its diagonal elements. The trace is invariant under similarity transformations and is useful in various matrix operations and proofs.
What matrix sizes are supported?
This calculator supports matrices of any size for trace and sum operations. For determinant calculation, it supports up to 3×3 matrices. For larger matrices or more complex operations, use specialized linear algebra software.
Calculator by
Prof. Emily Watson, PhD
PhD in Applied MathematicsStatistics Certification