What is a Matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are fundamental structures in linear algebra and mathematics, used to represent and solve complex systems of equations, perform transformations, and model real-world phenomena.
Matrix Definition and Structure
A matrix with m rows and n columns is called an m×n matrix. Each individual value in a matrix is called an element or entry. The element in row i and column j is typically denoted as aij. This notation system is standard in mathematical literature and academic research.
Types of Matrices
- Square Matrix: Same number of rows and columns (n×n)
- Identity Matrix: Square matrix with 1s on diagonal, 0s elsewhere
- Zero Matrix: All elements are zero
- Diagonal Matrix: Non-zero elements only on main diagonal
- Symmetric Matrix: Equal to its transpose (A = A^T)
Expert Note: This calculator implements standard matrix algorithms used in academic and professional settings. The determinant calculation uses cofactor expansion for 3×3 and 4×4 matrices, which is the most reliable method for educational purposes.