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Linear Algebra & Matrices Calculators
Work with matrices, vectors, linear systems, transformations, and decompositions. Start with the calculator matching the values you possess, then use related tools to verify or extend the result.
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Linear Algebra & Matrices topics
Select a topic to reveal its calculators. Multiple topics can remain open at the same time.Linear Algebra & MatricesWork with matrices, vectors, linear systems, transformations, and decompositions.59 available
Matrix basics and operations
- Matrix CalculatorPerform and compare common operations on one or two matrices.Open calculator
- Matrix Addition CalculatorAdd matrices with matching dimensions entry by entry.Open calculator
- Matrix Subtraction CalculatorSubtract matrices with matching dimensions entry by entry.Open calculator
- Matrix Multiplication CalculatorMultiply dimensionally compatible matrices in the correct order.Open calculator
- Matrix by Scalar CalculatorMultiply or divide every matrix entry by a scalar.Open calculator
- Matrix Transpose CalculatorExchange rows and columns to form a matrix transpose.Open calculator
- Matrix Power CalculatorRaise a square matrix to a supported integer power.Open calculator
- Matrix Trace CalculatorAdd the main-diagonal entries of a square matrix.Open calculator
- Matrix Determinant CalculatorCalculate the determinant of a square matrix.Open calculator
- Cofactor Expansion CalculatorEvaluate a determinant through a chosen Laplace expansion.Open calculator
- Matrix Minors & Cofactor Matrix CalculatorFind every minor, signed cofactor, and the resulting cofactor matrix.Open calculator
- Adjugate (Classical Adjoint) Matrix CalculatorTranspose the cofactor matrix to obtain the adjugate.Open calculator
- Inverse Matrix CalculatorCalculate an inverse when the square matrix is nonsingular.Open calculator
- Matrix Norm CalculatorCompare supported matrix norms with their definitions made explicit.Open calculator
- Hadamard Product CalculatorMultiply equally sized matrices entry by entry.Open calculator
- Kronecker (Tensor) Product CalculatorConstruct the block matrix produced by a Kronecker product.Open calculator
- Matrix Properties CalculatorClassify diagonal, triangular, symmetric, skew-symmetric, and orthogonal structure.Open calculator
Linear systems and row reduction
- Linear System SolverEnter coefficient matrix A and right-hand side b, then classify and solve Ax = b.Open calculator
- Gaussian Elimination CalculatorReduce a system to row echelon form and finish by back substitution.Open calculator
- Gauss-Jordan Elimination & RREF CalculatorContinue row reduction to reduced row echelon form with visible operations.Open calculator
- Cramer's Rule CalculatorSolve an eligible square system using determinant replacements.Open calculator
- Matrix Equation CalculatorSolve supported equations of the form AX = B or XA = B.Open calculator
- Least Squares Solution CalculatorFind a best-fit solution when a linear system has no exact solution.Open calculator
Vector spaces, bases, and transformations
- Matrix Rank CalculatorDetermine rank and identify pivot structure using a stated tolerance policy.Open calculator
- Null Space CalculatorFind a basis and dimension for the solutions of Ax = 0.Open calculator
- Column Space CalculatorFind a basis and dimension for a matrix's column space.Open calculator
- Row Space CalculatorFind a basis and dimension for a matrix's row space.Open calculator
- Basis & Dimension CalculatorExtract a basis from vectors and report the dimension of their span.Open calculator
- Linear Independence CalculatorTest whether vectors are linearly independent and explain the dependency result.Open calculator
- Linear Combination & Span CalculatorTest whether a target belongs to a span and find coefficients when possible.Open calculator
- Change of Basis CalculatorBuild a transition matrix between two ordered bases.Open calculator
- Coordinates in a Basis CalculatorExpress a vector through coordinates relative to an ordered basis.Open calculator
- Linear Transformation Matrix CalculatorConstruct or apply the matrix representation of a linear transformation.Open calculator
- Orthogonal Complement CalculatorFind a basis for the orthogonal complement of a finite-dimensional subspace.Open calculator
- Projection Matrix CalculatorBuild the matrix that projects onto a specified subspace.Open calculator
- Gram-Schmidt CalculatorTurn independent vectors into an orthogonal or orthonormal basis.Open calculator
Eigenvalues and decompositions
- Eigenvalue & Eigenvector CalculatorFind eigenvalues, eigenspaces, and associated eigenvectors.Open calculator
- Characteristic Polynomial CalculatorCalculate det(λI − A) using a clearly stated sign convention.Open calculator
- Matrix Diagonalization CalculatorFind P and D when a matrix satisfies A = PDP⁻¹.Open calculator
- LU Decomposition CalculatorFactor a matrix into lower and upper triangular factors with pivoting shown.Open calculator
- QR Decomposition CalculatorFactor a matrix into orthogonal and upper-triangular factors.Open calculator
- Cholesky Decomposition CalculatorFactor an eligible positive-definite matrix as LLᵀ or LLᴴ.Open calculator
- LDLᵀ Decomposition CalculatorFactor an eligible symmetric matrix into L, D, and Lᵀ factors.Open calculator
- Singular Value Decomposition CalculatorFactor a matrix into UΣVᵀ and verify the reconstruction.Open calculator
- Singular Values CalculatorCalculate and order the singular values without requiring the full SVD display.Open calculator
- Matrix Pseudoinverse CalculatorCalculate the Moore-Penrose pseudoinverse of a supported matrix.Open calculator
- Polar Decomposition CalculatorFactor a matrix into orthogonal or unitary and positive-semidefinite parts.Open calculator
- Schur Decomposition CalculatorCompute a unitary or orthogonal Schur factorization of a square matrix.Open calculator
- Jordan Normal Form CalculatorFind Jordan blocks and a similarity transform when the computation is supported.Open calculator
Vectors and products
- Vector Addition & Subtraction CalculatorAdd or subtract vectors component by component.Open calculator
- Dot Product CalculatorCalculate the scalar product of two equal-dimensional vectors.Open calculator
- Cross Product CalculatorCalculate the three-dimensional vector product with orientation preserved.Open calculator
- Vector Magnitude CalculatorFind a vector's Euclidean length from its components.Open calculator
- Unit Vector CalculatorNormalize a nonzero vector while preserving its direction.Open calculator
- Vector Projection CalculatorFind scalar and vector projections of one vector onto another.Open calculator
- Scalar Triple Product CalculatorCalculate a · (b × c) and interpret the signed volume.Open calculator
Numerical properties and advanced matrices
- Matrix Condition Number CalculatorMeasure sensitivity under an explicitly selected matrix norm.Open calculator
- Positive Definite Matrix CalculatorTest positive definiteness or semidefiniteness under stated assumptions.Open calculator
- Matrix Exponential CalculatorEvaluate eᴬ with the numerical method and precision disclosed.Open calculator