Online Matrix Calculator: Determinant, Inverse, RREF, LU, Eigenvalues
A matrix calculator for two matrices A and B up to 6×6. Run addition, subtraction and multiplication; scale, transpose and find the determinant, inverse, RREF, rank, LU decomposition and eigenvalues/eigenvectors. Edit cells directly, fill with random or identity values, paste matrices in bulk, and copy A, B or the result — all computed privately in your browser.
Matrix Calculator Guide
Arithmetic, determinant, inverse, RREF, rank, LU and eigenvalues
The matrix calculator performs common linear-algebra operations on matrices up to 6×6. Fill in matrix A (and matrix B for binary operations), choose an operation, and press Compute. It supports addition, subtraction, multiplication, scalar multiplication, transpose, determinant, inverse, reduced row echelon form, rank, LU decomposition and eigenvalues/eigenvectors.
01 Entering matrices
Use the rows and cols inputs to set the dimensions of A (1×1 to 6×6). Click Random to fill A with random values (handy for quick tests) or Identity to set A to the identity matrix. Type values directly into cells. For operations that need two matrices (A + B, A − B, A × B), matrix B appears with its own size controls, Random and Identity buttons.
Choose an operation from the button bar. Operations requiring B will show matrix B; the Scale operation reveals a scalar field. Press Compute to run the selected operation. The result is shown as text — either a matrix, a scalar (for det/rank), or eigenvalues with their eigenvectors.
- Matrices can be rectangular (non-square) for add, sub, scale and transpose
- Determinant, inverse and eigenvalues require a square matrix
- Multiplication A × B requires A’s columns to equal B’s rows
- A singular matrix has no inverse and a determinant of zero
Matrix A
- rows / colsSet the dimensions of matrix A (1–6).
- RandomFill A with random values.
- IdentitySet A to the identity matrix (square only).
- cellsEditable entries of matrix A.
- text box (A)Paste or type the whole matrix, one row per line, values separated by commas or spaces; brackets are optional.
- Apply (A)Parses the text box and resizes/fills matrix A in one step.
- Copy (A)Copies matrix A as bracket rows for pasting into a spreadsheet or another tool.
Matrix B (binary ops)
- rows / colsSet the dimensions of matrix B.
- RandomFill B with random values.
- IdentitySet B to the identity matrix.
- cellsEditable entries of matrix B.
- text box (B)Paste or type matrix B, one row per line (commas or spaces; brackets optional).
- Apply (B)Parses the text box and resizes/fills matrix B in one step.
- Copy (B)Copies matrix B as bracket rows.
Operation buttons
- A + BElement-wise addition (requires matching sizes).
- A − BElement-wise subtraction (requires matching sizes).
- A × BMatrix multiplication (A-cols = B-rows).
- Scale AMultiply every element of A by the scalar.
- Transpose ASwap rows and columns of A.
- det(A)Determinant of square A.
- A⁻¹Inverse of square, non-singular A.
- RREF(A)Reduced row echelon form of A.
- rank(A)Rank (number of independent rows).
- LU(A)LU decomposition into lower/upper factors.
- Eigen(A)Eigenvalues and eigenvectors of square A.
Run
- scale factorScalar value used by the Scale A operation.
- ComputeRuns the selected operation and displays the result.
- Copy (result)Copies the full result text (matrix, determinant, LU factors or eigenvalues) to the clipboard.
- Use Identity and Random to quickly set up textbook examples.
- If inverse or eigenvalue fails, check that the matrix is square and (for inverse) non-singular.
- RREF is useful both for solving systems and checking linear independence.
- Eigenvalues may be complex; the output shows them as computed.
A free online matrix calculator for matrices up to 6×6. Add, subtract and multiply matrices, multiply by a scalar, transpose, compute the determinant, inverse, reduced row echelon form (RREF), rank, LU decomposition and symmetric eigenvalues. Adjust dimensions, fill random or identity values, and read results instantly. All algebra runs locally in your browser.
Entering matrices
Set the dimensions of A (and B for binary operations) and fill in values, or use the random and identity quick-fill buttons. Choose an operation from the control panel; results appear below for both single-matrix operations (determinant, inverse, transpose, RREF, rank, LU, eigenvalues) and two-matrix operations (A+B, A−B, A×B).
Supported operations
Addition, subtraction, multiplication, scalar multiplication, transpose, determinant, inverse, reduced row echelon form (Gaussian elimination with partial pivoting), rank, LU decomposition and symmetric eigenvalue decomposition via Jacobi rotation. Eigenvalues are computed for the symmetric part (A+Aᵀ)/2, which is an approximation for non-symmetric matrices.
Use cases and limits
Handy for linear-algebra homework, checking hand calculations and quick engineering work. Matrices are limited to 6×6 to keep the interface focused; very ill-conditioned matrices may show small numerical residuals. All computations use local JavaScript and no matrix is uploaded.
FAQ
QWhat is the maximum matrix size?
6×6 for both A and B; dimensions can be changed independently for binary operations.
QWhich operations are supported?
Add, subtract, multiply, scalar multiply, transpose, determinant, inverse, RREF, rank, LU decomposition (partial pivoting) and symmetric eigenvalues.
QHow are eigenvalues calculated?
By Jacobi rotation on the symmetric part (A+Aᵀ)/2. For non-symmetric matrices this is an approximation; use a dedicated numerical package for exact non-symmetric spectra.
QAre my matrices saved or uploaded?
No. All matrix arithmetic runs in your browser; nothing is sent to a server or stored in history.