Matrix Calculator

  • LU Decomposition Calculator with Partial Pivoting
    Free LU decomposition calculator with partial pivoting. Factor a square matrix into L and U with row pivot vector P so that P*A = L*U, plus the determinant.
  • Hadamard Product (Element-wise Matrix Product) Calculator
    Compute the Hadamard product C = A ∘ B of two equal-size matrices: each entry c_jk = a_jk × b_jk. Element-wise (Schur) multiplication with adjustable display precision.
  • Matrix Rank Calculator
    Compute the rank of any real matrix A online. Enter your m x n matrix and get the number of linearly independent rows or columns via Gaussian elimination.
  • Matrix Norm Calculator
    Compute four matrix norms of any real n x m matrix: L1 (max column sum), L2/spectral (largest singular value), Frobenius, and L-infinity (max row sum).
  • Matrix-Vector Product Calculator
    Compute the product c = A·x of a matrix A and a column vector x. Enter any rows×cols matrix and a vector; get the resulting column vector instantly.
  • Vector Scalar Multiplication Calculator
    Multiply every component of an n-dimensional vector by a scalar lambda. Computes c = lambda*a element-wise, returning a vector of the same dimension.
  • Vector Outer Product Calculator
    Compute the outer product (tensor/dyadic product) of two vectors a and b. Enter components to get the full m x n matrix C where C[i][j] = a_i * b_j.
  • Adjoint Matrix (Hermitian Conjugate / Conjugate Transpose) Calculator
    Compute the adjoint matrix A* (Hermitian conjugate / conjugate transpose) of any real or complex m x n matrix. Transpose then conjugate, with worked example.
  • Matrix Addition and Subtraction Calculator
    Add or subtract two matrices A and B element-by-element. Compute A+B, A-B, or B-A for any m x n matrices up to 6x6, with adjustable display precision.
  • Matrix Multiplication (Product) Calculator
    Multiply two matrices online. Compute the matrix product C = A.B or B.A with full conformability checking and a clean row-by-row result.
  • Matrix Scalar Multiplication Calculator
    Multiply every element of a matrix A by a scalar lambda to get the result matrix C. Supports any size up to 10x10, negatives, decimals and scientific notation.
  • Cramer's Rule Calculator
    Solve 2×2 and 3×3 linear systems with Cramer's Rule. Enter matrix A and vector b to get x, y, z plus every determinant used. Free and instant.
  • Matrix Condition Number Calculator
    Compute the spectral (2-norm) condition number κ(A) of a 2×2 matrix as the ratio of its largest to smallest singular value, plus singular values and determinant.
  • n×n Matrix Determinant Calculator
    Compute the determinant det(A) of any square n×n matrix (1 to 10) and its reciprocal 1/det(A). Uses Gaussian elimination; flags singular matrices.
  • Inverse Matrix Calculator
    Find the inverse of a 2×2 or 3×3 matrix instantly. Computes the determinant, adjugate, and inverse A⁻¹ = adj(A)/det(A) with full steps.
  • Matrix Trace Calculator
    Calculate the trace of a square matrix (2×2, 3×3 or 4×4) by summing its main diagonal entries. Fast, free, and shows the formula tr(A)=Σ Aᵢᵢ.
  • Matrix Multiplication Calculator
    Multiply two 2×2 matrices instantly. Enter each element of matrix A and B to get the product matrix AB using the row-by-column dot product rule.
  • 3x3 Matrix Determinant Calculator
    Calculate the determinant of a 3x3 matrix and its reciprocal (1/det A) using cofactor expansion. Enter nine real entries; detects singular matrices.
  • Matrix by Scalar Calculator
    Multiply a 2×2 matrix by a scalar instantly. Enter your scalar and matrix entries to compute cA element-by-element with this free calculator.
  • Hadamard Product Calculator
    Compute the Hadamard (element-wise) product of two matrices. Enter dimensions and values to get A∘B where each entry is A_ij × B_ij.
  • Quaternion Calculator
    Free quaternion calculator: compute the Hamilton product q1×q2, the norm (magnitude), and the conjugate of two 4-component quaternions instantly.
  • 3x3 Matrix Inverse Calculator
    Compute the inverse of any 3x3 matrix online. Enter nine real numbers and get A^-1 plus the determinant, with singular-matrix detection.
  • Inverse of an n×n Matrix (via LU Decomposition)
    Compute the inverse of a square n×n matrix online using LU decomposition with partial pivoting. Enter your matrix, get A^-1, determinant and singularity check.
  • N-by-N System of Linear Equations Solver (LU Decomposition)
    Solve a system of n linear equations in n unknowns A·x = b. Uses LU decomposition with partial pivoting for the unique solution vector x and determinant.

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