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Linear Algebra & Matrices Calculators
Work with matrices, vectors, linear systems, transformations, and decompositions. Use this collection when 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