Linear Algebra calculators
36 calculators Matrix Calculator Free matrix calculator for 2x2 and 3x3 matrices. Compute determinant, inverse, transpose, trace, adjugate, cofactors, and rank with step-by-step working.
Open Adjoint Matrix Calculator Calculate the adjoint (adjugate) of a 2x2, 3x3, or 4x4 matrix instantly. Shows cofactor matrix, determinant, inverse, and every step of the working.
Open Characteristic Polynomial Calculator Find the characteristic polynomial p(lambda) = det(A - lambdaI) for 2x2, 3x3 or 4x4 matrices. Get eigenvalues, trace, determinant, and full step-by-step working.
Open Cholesky Decomposition Calculator Compute the Cholesky factorization A = LL^T for 2x2 and 3x3 symmetric positive-definite matrices. See every step, the LDL decomposition, and the verification check.
Open Cofactor Expansion Calculator Calculate the determinant of any 2x2, 3x3, or 4x4 matrix using cofactor (Laplace) expansion. See every minor, sign, and cofactor term worked out step by step.
Open Cofactor Matrix Calculator Find the cofactor matrix of any 2x2, 3x3, or 4x4 matrix instantly. Shows minors, signs, the adjugate matrix, and a full step-by-step breakdown.
Open Column Space Calculator Find the column space (Col A) of any matrix up to 4x4 instantly. Shows basis vectors, rank, and dimension with a full step-by-step RREF solution.
Open Condition Number Calculator Calculate the condition number of a 2x2 or 3x3 matrix with four norm choices (1, 2, infinity, Frobenius). Shows matrix norm, inverse norm, and a worked step-by-step solution.
Open Corner Point Calculator: Linear Programming Feasible Region Solver Find all corner points of a linear program. Enter the objective function and constraints, get every vertex with its P value and the optimal solution shown step by step.
Open Cramer's Rule Calculator Solve any 2x2 or 3x3 linear system using Cramer's rule. Enter coefficients to get x, y, z with full determinant steps shown instantly.
Open Diagonalize Matrix Calculator Diagonalize any 2x2 or 3x3 matrix instantly. Get eigenvalues, eigenvectors, the P and D matrices, and a full step-by-step verification of A = PDP-1.
Open Eigenvalue and Eigenvector Calculator Find eigenvalues, eigenvectors, the characteristic polynomial, trace, determinant, and diagonalizability for any 2x2 or 3x3 matrix with step-by-step solutions.
Open Gauss-Jordan Elimination Calculator Solve 2x2, 3x3, or 4x4 linear systems with full Gauss-Jordan elimination. See every row operation, the RREF matrix, rank, nullity, and the solution instantly.
Open Gram-Schmidt Calculator Compute the orthogonal and orthonormal basis of up to 4 vectors in up to 4 dimensions using the Gram-Schmidt process, with a full step-by-step breakdown.
Open Hadamard Product Calculator Calculate the Hadamard (element-wise) product of two matrices instantly. Supports 1x1 to 4x4, shows step-by-step work, properties, and Frobenius norms.
Open Inverse Matrix Calculator Find the inverse of a 2x2 or 3x3 matrix instantly. Shows determinant, adjugate, step-by-step cofactor work, and whether the matrix is singular.
Open Linear Combination Calculator Solve any 2x2 system of linear equations using the elimination method. Get x and y instantly, with a full step-by-step worked solution and special-case detection.
Open Linear Independence Calculator Test whether a set of vectors is linearly independent or dependent. Uses Gaussian elimination to find rank, pivot count, and span dimension with step-by-step work.
Open LU Decomposition Calculator Compute the LU decomposition of any 2x2 or 3x3 matrix instantly. Shows L, U and P matrices, the determinant, and every elimination step. Free online tool.
Open Matrix Addition and Subtraction Calculator Add or subtract two matrices of any size from 2x2 to 4x4. Get the result matrix and a full element-by-element step-by-step solution instantly.
Open Matrix by Scalar Calculator Multiply a 2x2 matrix by any scalar instantly. Get the full result matrix plus a step-by-step solution showing every multiplication. Free online linear algebra tool.
Open Matrix Determinant Calculator Calculate the determinant of a 2x2, 3x3, or 4x4 matrix instantly. See cofactor expansion steps, trace, rank, and whether the matrix is invertible.
Open Matrix Multiplication Calculator Multiply two matrices (up to 4x4) instantly with full step-by-step dot-product working. Covers 2x2, 2x3, 3x3, 3x4, and more. Free, no sign-up required.
Open Matrix Norm Calculator Calculate all five standard matrix norms instantly: 1-norm, infinity norm, Frobenius norm, spectral 2-norm, and max norm for any matrix up to 4x4.
Open Matrix Power Calculator Raise any 2x2, 3x3, or 4x4 square matrix to a positive, zero, or negative integer power. See the resulting matrix, determinant, trace, and full step-by-step working.
Open Matrix Rank Calculator Find the rank of any matrix (up to 4x4) using Gaussian elimination. See every row operation, the pivot positions, nullity, and a plain-English interpretation.
Open Matrix Trace Calculator Calculate the trace of any square matrix up to 6x6 instantly. Shows diagonal elements, step-by-step working, key properties, and the eigenvalue-sum relationship.
Open Matrix Transpose Calculator Transpose any matrix up to 6x6 instantly. Enter integers, decimals, or fractions. See the transposed matrix, step-by-step working, and key properties.
Open Null Space Calculator Find the null space (kernel), nullity, and rank of any matrix up to 4x4. Shows RREF steps, basis vectors, and the parametric solution with full working.
Open Polar Decomposition Calculator Decompose any real 2x2 or 3x3 matrix into U (orthogonal) and P (positive semi-definite) factors. Shows singular values, step-by-step SVD work, and residual.
Open Pseudoinverse Calculator Calculate the Moore-Penrose pseudoinverse of any matrix online. Supports full column rank, full row rank, and SVD for rank-deficient cases, with step-by-step working.
Open QR Decomposition Calculator Factor any matrix A = QR instantly. Enter up to a 4x4 matrix and get the orthogonal Q matrix, upper-triangular R, step-by-step Gram-Schmidt work, and a verification check.
Open Reduced Row Echelon Form (RREF) Calculator Calculate the RREF or REF of any matrix step by step. Supports 2x2 to 4x5 matrices, exact fractions, and interprets unique, infinite, or no-solution systems.
Open Singular Values Calculator Calculate singular values of any 2x2 or 3x3 matrix with full SVD decomposition: U, Sigma, V-transpose, matrix rank, condition number, and Frobenius norm, step by step.
Open SVD Calculator - Singular Value Decomposition Compute the singular value decomposition A = U*Sigma*V^T of any 2x2 or 3x3 real matrix, with singular values, rank, condition number, and step-by-step working.
Open Tensor Product Calculator Compute the tensor product (Kronecker product) A x B of any two matrices. Shows the result matrix, block expansion steps, dimensions, Frobenius norm, and rank.
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