Matrix Calculator

  • RREF Matrix Calculator
    Enter a matrix and instantly compute its reduced row echelon form (RREF). Paste values and get the RREF matrix for quick checks and study.
  • 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.
  • 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.
  • 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.
  • Matrix Power (Aⁿ) Calculator
    Compute the n-th power of a square matrix A (Aⁿ = A·A·…·A) for 2x2, 3x3 or 4x4 matrices. Supports n = 0 (identity) and negative powers via the inverse.
  • 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).
  • 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 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 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.
  • 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.
  • 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.
  • Angle Between Two Vectors Calculator
    Find the angle between two 2D or 3D vectors using the dot product formula. Get the result in degrees and radians, plus magnitudes and cos θ.
  • System of Equations Calculator
    Solve a 2-variable linear system a₁x+b₁y=c₁, a₂x+b₂y=c₂ instantly using Cramer's rule. Detects parallel/identical lines with no unique solution.
  • 2x2 Matrix Inverse Calculator
    Compute the inverse of a 2x2 matrix instantly. Enter a, b, c, d to get the determinant and each element of A⁻¹, with a singular-matrix check.
  • 2x2 Eigenvalue Calculator
    Find the eigenvalues of any 2x2 matrix instantly. Handles real and complex conjugate eigenvalues using the trace and determinant formula.
  • 2×2 Matrix Multiplication Calculator
    Multiply two 2×2 matrices instantly. Enter the 8 entries of matrices A and B to get the product C = A·B with full step-by-step results.
  • 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.
  • Adding & Subtracting Vectors Calculator
    Add or subtract two 2D vectors to find the resultant magnitude and direction (angle). Computes Rx, Ry, magnitude √(Rx²+Ry²) and θ via atan2.
  • 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.
  • 3×3 Matrix Eigenvalue Calculator
    Find the eigenvalues of any 3×3 matrix instantly. Solves the characteristic cubic det(A−λI)=0 with Cardano's method and lists λ₁, λ₂, λ₃.

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