Matrix Calculator

Our Matrix Calculator supports all fundamental operations: matrix addition and subtraction, matrix multiplication, scalar multiplication, transposition, determinant calculation, matrix inversion, eigenvalue and eigenvector computation, decompositions (LU, QR, SVD), rank and trace calculation. We also support advanced operations like matrix power and solving linear systems.

You can enter a matrix directly in the interactive grid. Click on cells to edit values. Use the + and - buttons to increase or decrease the matrix dimensions (rows and columns). You can also use presets to quickly generate identity, zero, random or diagonal matrices with the current dimensions.

A matrix is invertible (or non-singular) if its determinant is non-zero. Only square matrices can be invertible. If a matrix is singular (determinant = 0), it has no inverse. The calculator automatically shows whether the matrix is invertible in the properties displayed below the matrix.

Eigenvalues are scalar values λ such that A·v = λ·v, where A is the matrix and v is the corresponding eigenvector. The calculator automatically computes all eigenvalues and their corresponding eigenvectors for square matrices. These are fundamental for understanding linear transformations and are used in many scientific and engineering applications.

We support three main decompositions: LU (Lower-Upper) for efficient solving of linear systems, QR for least squares solutions and eigenvalue analysis, and SVD (Singular Value Decomposition) for data analysis and compression. Each decomposition has specific applications in computational linear algebra.

Yes! You can switch to "Two Matrices" mode to work with two matrices (A and B) simultaneously. This allows you to perform operations like A + B, A - B, A × B, and compare the properties of both matrices. Single mode is useful for operations on a single matrix like determinant, inverse, eigenvalues, etc.

The displayed properties include: Determinant (for square matrices only), Rank (dimension of the column/row space), Trace (sum of diagonal elements, for square matrices only), and Dimensions. Additionally, badges are shown for special properties like Square, Symmetric, Diagonal, Identity, and Invertible.

The calculator supports matrices from 1×1 up to 10×10. This range covers most practical applications in linear algebra. For larger matrices, we recommend using specialized software. Operations are optimized for performance and precision within the supported range.

You can solve linear systems of the form Ax = b using matrix operations. If A is invertible, the solution is x = A^(-1) × b. The calculator can compute the inverse of A and multiply it by the vector b. Make sure the coefficient matrix is square and invertible to have a unique solution.