Angle Between Vectors Calculator - Calculate the angle between two 2D or 3D vectors using the dot product formula cos(θ) = (a·b)/(|a||b|). Get step-by-step solutions, results in both degrees and radians, interactive vector diagram, and geometric interpretation. New

Characteristic Polynomial Calculator - Calculate the characteristic polynomial det(A − λI) of a square matrix. Supports 2×2 to 6×6 matrices with step-by-step cofactor expansion, eigenvalue extraction, coefficient analysis, and interactive polynomial visualization. New

Cholesky Decomposition Calculator - Decompose a symmetric positive-definite matrix into A = LLᵀ with animated step-by-step computation. See each element of the lower-triangular matrix L derived with full formulas, verify the result, and explore the factorization visually. New

Column Space Calculator - Find the column space and basis of any matrix using row reduction. See each row operation step by step with pivot column highlighting, rank, dimension, and interactive visualization for 2D/3D column spaces. New

Cramer's Rule Calculator - Solve systems of 2 or 3 linear equations using Cramer's rule. Enter coefficients, get step-by-step determinant calculations with animated matrix visualization, geometric interpretation graph, and the complete solution. New

Cross Product Calculator - Calculate the cross product (vector product) of two 3D vectors using the determinant formula. Get step-by-step expansion, the perpendicular result vector, its magnitude (parallelogram area), direction verification, and an interactive 3D visualization. New

Determinant Calculator - Calculate the determinant of any square matrix with detailed step-by-step cofactor expansion, matrix properties analysis, and visual solutions.

Dot Product Calculator - Calculate the dot product (scalar product) of two vectors in 2D, 3D, or higher dimensions. Get the angle between vectors, magnitudes, scalar and vector projections, geometric interpretation, and step-by-step formulas with an interactive vector diagram. New

Eigenvalue and Eigenvector Calculator - Calculate eigenvalues and eigenvectors of 2x2 and 3x3 matrices with detailed step-by-step solutions, characteristic polynomial derivation, interactive visualization, and matrix property analysis.

Gram-Schmidt Calculator - Orthonormalize a set of linearly independent vectors using the Gram-Schmidt process. Get step-by-step projections, orthogonal and orthonormal bases, verification of orthogonality, and an interactive vector visualization. New

Jacobian Matrix Calculator - Calculate the Jacobian matrix of multivariable vector-valued functions. Enter transformation components like F(x,y) = (x²+y, xy), get the full Jacobian matrix with all partial derivatives, the determinant, eigenvalues, step-by-step solution with MathJax, and an interactive grid deformation visualization showing how the transformation distorts space. New

Matrix Calculator - Calculate matrix operations with step-by-step solutions: addition, subtraction, multiplication, inverse, transpose, and determinant. Visual matrix display with detailed explanations.

Matrix Diagonalization Calculator - Diagonalize a square matrix by computing eigenvalues, eigenvectors, and the decomposition A = PDP⁻¹. Supports 2×2 to 5×5 matrices with step-by-step solutions, characteristic polynomial, multiplicity analysis, and interactive visualization. New

Matrix Inverse Calculator - Calculate the inverse of a square matrix using Gauss-Jordan elimination with detailed step-by-step row operations. Supports 2×2 to 6×6 matrices with exact fractional arithmetic, determinant calculation, and A×A⁻¹=I verification. New

Matrix LU Decomposition Calculator - Calculate LU decomposition of any square matrix with partial pivoting. Get lower triangular (L), upper triangular (U), and permutation (P) matrices with step-by-step Gaussian elimination and verification. New

Matrix Multiplication Calculator - Multiply two matrices with detailed step-by-step element computation. See each dot product broken down, with color-coded row × column visualization. Supports matrices up to 5×5 with interactive dimension controls. New

Matrix Power Calculator - Calculate the power of a square matrix A raised to any integer exponent n. See each multiplication step animated, intermediate matrices A¹ through Aⁿ, determinant and trace properties, with MathJax formulas and interactive visualization. New

Matrix Rank Calculator - Calculate the rank of any matrix using Gaussian elimination (row echelon form). Get step-by-step row reduction, pivot analysis, column space and null space dimensions, and visual heatmap. Supports matrices up to 10×10. New

Matrix Trace Calculator - Calculate the trace of a square matrix (sum of diagonal elements), verify its equality with the sum of eigenvalues, explore trace properties, and visualize the diagonal with an interactive heatmap. Supports matrices up to 10×10. New

Null Space Calculator - Find the null space (kernel) of any matrix by solving Ax = 0 using Gaussian elimination. Get the basis vectors, nullity, step-by-step RREF reduction, and rank-nullity theorem verification with exact fractional arithmetic. New

Partial Fraction Decomposition Calculator - Decompose rational functions into partial fractions with detailed step-by-step solutions, coefficient analysis, and visual decomposition breakdown.

QR Decomposition Calculator - Decompose any matrix A into an orthogonal matrix Q and upper triangular matrix R using the Gram-Schmidt process. Supports 2×2 to 5×5 matrices with animated step-by-step orthogonalization, orthogonality verification QᵀQ = I, and interactive visualization. New

RREF Calculator (Row Echelon Form) - Reduce any matrix to reduced row echelon form (RREF) with detailed step-by-step row operations. Enter your matrix, see every pivot, swap, and elimination step visualized. Identify rank, nullity, pivot columns, free variables, and solution type instantly. New

Singular Value Decomposition (SVD) Calculator - Calculate the Singular Value Decomposition (SVD) of any matrix. Decompose A = UΣVᵀ with step-by-step solutions, interactive 3D visualization, rank analysis, condition number, and applications in data compression and dimensionality reduction. New

Unit Vector Calculator - Calculate the unit vector (normalized vector) in the direction of a given 2D, 3D, or n-dimensional vector. Get the magnitude, each normalized component, direction angles, step-by-step normalization process, and visual verification that the result has length 1. New

Vector Calculator - Free online vector calculator with step-by-step solutions. Calculate dot product, cross product, magnitude, unit vector, angle between vectors, projection, and more with interactive 3D visualization.

Vector Magnitude Calculator - Calculate the magnitude (length or Euclidean norm) of a 2D, 3D, or n-dimensional vector. Get step-by-step computation showing each squared component, the sum under the radical, and the final square root result, with an interactive vector diagram. New

Vector Projection Calculator - Calculate the vector projection and scalar projection of one vector onto another. Supports 2D and 3D vectors with step-by-step formulas, interactive diagram, and orthogonal decomposition. New