Determinant, cross product, dot product, and eigenvalue calculators. Browse our free linear algebra tools below — all calculators are instant, accurate, and require no sign-up.
Adjoint (Adjugate) Matrix Calculator — Compute the classical adjoint (adjugate) matrix with cofactors, minors, sign pattern visualization, inverse connection, and verification that A·adj(A) = det(A)·I.
Cholesky Decomposition Calculator — Factor a symmetric positive definite matrix A = LLᵀ with step-by-step Cholesky algorithm, positive definiteness check, solve Ax=b, and verification display.
Cramer's Rule Calculator — Solve 2×2, 3×3, and 4×4 systems of linear equations using Cramer's Rule with determinant calculations, step-by-step Dx/Dy/Dz display, solution verification, and determinant comparison visualization.
Cross Product Calculator — 3D Vector Cross Product & Area — Compute the cross product of two 3D vectors, find the parallelogram area, unit normal direction, angle between vectors, and scalar triple product with step-by-step breakdowns.
Matrix Determinant Calculator — Compute the determinant for 2×2 through 5×5 matrices with cofactor expansion steps, minor matrix display, term contribution bars, and comprehensive properties table.
Eigenvalue & Eigenvector Calculator — Compute eigenvalues and eigenvectors for 2×2 and 3×3 matrices with characteristic polynomial, diagonalization check, spectrum visualization, and detailed calculation steps.
Dot Product Calculator — Angle, Orthogonality & Projection — Compute the dot product of two vectors in 2D–6D, find the angle between them, check orthogonality and parallelism, and visualize component contributions with an interactive calculator.
Gram-Schmidt Orthogonalization Calculator — Apply the Gram-Schmidt process to 2–4 vectors in R², R³, or R⁴. View step-by-step projections, orthonormal results, dot-product verification matrix, and norm comparison bars.
Gauss-Jordan Elimination Calculator — Solve systems of linear equations Ax=b via augmented matrix Gauss-Jordan elimination with step-by-step row operations, back substitution display, and solution visualization.
Hadamard Product Calculator — Calculate the Hadamard (element-wise) product of two matrices. Compare with standard multiplication, view properties, and explore visual breakdowns.
LU Decomposition Calculator — Factor a square matrix into lower and upper triangular matrices A=LU with step-by-step Doolittle method, solve Ax=b via forward/back substitution, and verification display.
Matrix Calculator — Perform matrix operations including addition, subtraction, multiplication, transpose, determinant, inverse, and scalar multiplication for matrices up to 5×5.
Matrix Addition & Subtraction Calculator — Add or subtract matrices up to 5×5 with element-wise breakdown, scalar combination mode, Frobenius norms, comparison heat map, and detailed result tables.
Matrix Scalar Multiplication Calculator — Multiply a matrix by a scalar with element-wise display, property verification, chain operations, determinant/trace scaling, and before/after visualization.
Matrix Inverse Calculator — Find the inverse of a matrix up to 5×5 using the cofactor/adjugate method, with step-by-step cofactor table, verification A×A⁻¹=I, condition number analysis, and singular detection.
Matrix Norm Calculator — Compute Frobenius, spectral, 1-norm, infinity-norm, and max-norm of a matrix with comparison bars, relationship verification, and breakdown tables.
Matrix Multiplication Calculator — Multiply matrices up to 5×5 with dimension compatibility check, partial products breakdown, Strassen complexity comparison, and result magnitude visualization.
Matrix Trace Calculator — Compute the trace of a square matrix with property verification, eigenvalue connection, diagonal contribution bars, and two-matrix mode for cyclic property testing.
Matrix Rank Calculator — Compute the rank of a matrix up to 5×5 via row echelon form with nullity, rank-nullity theorem verification, pivot visualization, and step-by-step row reduction.
Null Space (Kernel) Calculator — Find the null space of a matrix via RREF with basis vectors, dimension, solution verification, step-by-step reduction, and component visualization.
Matrix Transpose Calculator — Transpose a matrix up to 5×5 with symmetry checks, skew-symmetric detection, double transpose verification, before/after display, and properties table.
Polar Decomposition Calculator — Decompose a matrix A = UP into a unitary factor U and positive semi-definite factor P. View singular values, condition number, and geometric interpretation.
QR Decomposition Calculator — Compute QR decomposition via Gram-Schmidt. View orthogonal Q and upper triangular R with step-by-step process, verification, and application reference.
Pseudoinverse Calculator — Compute the Moore-Penrose pseudoinverse of rectangular or singular matrices via SVD. Verify all four Moore-Penrose conditions with step-by-step details.
SVD Calculator — Compute the Singular Value Decomposition A = UΣVᵀ. View singular values, rank, condition number, matrix norms, energy distribution, and low-rank approximation.
Row Echelon Form (REF & RREF) Calculator — Transform any matrix to Row Echelon Form and Reduced Row Echelon Form with step-by-step row operations, pivot identification, rank determination, and visual pivot highlighting.
Unit Vector Calculator — Normalize Any 2D–6D Vector — Compute the unit vector (normalization) of any vector from 2D to 6D. Verify ‖û‖ = 1, see direction angles, component contributions, scaling, and compare original vs unit vector visually.
Vector Addition & Subtraction Calculator — Add or subtract 2–5 vectors in 2D or 3D. View resultant magnitude, direction, component-wise breakdown table, magnitude comparison bars, and component contribution visuals.
Vector Direction Calculator — Angles, Cosines & Azimuth — Compute direction angles α, β, γ from a 2D or 3D vector, direction cosines, azimuth/elevation, compass visualization, angle bars, and direction cosine identity verification.