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.
Free Linear Algebra Calculators
34 toolsDeterminant, cross product, dot product, and eigenvalue calculators. Browse our free linear algebra tools below — no sign-up required.
Angle Between Two Vectors Calculator — Degrees, Radians & Classification
Find the angle between two vectors in 2D–6D using the dot product formula. Get degrees, radians, cos/sin/tan θ, perpendicularity and parallelism checks, computation steps, and a visual angle gauge.
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.
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.
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.
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.
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.
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 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 Calculator
Perform matrix operations including addition, subtraction, multiplication, transpose, determinant, inverse, and scalar multiplication for matrices up to 5×5.
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.
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 Multiplication Calculator
Multiply matrices up to 5×5 with dimension compatibility check, partial products breakdown, Strassen complexity comparison, and result magnitude visualization.
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 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.
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 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 Transpose Calculator
Transpose a matrix up to 5×5 with symmetry checks, skew-symmetric detection, double transpose verification, before/after display, and properties table.
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.
Order of Magnitude Calculator — Powers of 10, Scientific Notation & Scale
Determine the order of magnitude of any number, convert to scientific notation, compare magnitudes, see the SI prefix region, and explore a logarithmic scale with real-world examples.
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.
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.
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.
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.
SVD Calculator
Compute the Singular Value Decomposition A = UΣVᵀ. View singular values, rank, condition number, matrix norms, energy distribution, and low-rank approximation.
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 Calculator — Magnitude, Unit Vector & Scalar Multiplication
Compute vector magnitude, unit vector, scalar multiplication, direction angles, and negation for 2D and 3D vectors with component visualization bars and properties table.
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.
Vector Magnitude Calculator — L1, L2 & L∞ Norms
Compute vector magnitude for 2D to 6D vectors using L1 (Manhattan), L2 (Euclidean), L∞ (Chebyshev), and custom Lp norms with unit vector, component contribution bars, and norm comparison.
Vector Projection Calculator — Projection, Rejection & Angle
Project vector a onto vector b: scalar projection, vector projection, rejection, angle between vectors, decomposition table, visual breakdown, and orthogonality verification.