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Vector Scalar Multiplication CalculatorMultiply every component of an n-dimensional vector by a scalar lambda. Computes c = lambda*a element-wise, returning a vector of the same dimension.
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Vector Outer Product CalculatorCompute 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.
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RREF Matrix CalculatorEnter a matrix and instantly compute its reduced row echelon form (RREF). Paste values and get the RREF matrix for quick checks and study.
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Matrix Scalar Multiplication CalculatorMultiply 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.
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Matrix Multiplication (Product) CalculatorMultiply two matrices online. Compute the matrix product C = A.B or B.A with full conformability checking and a clean row-by-row result.
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Cramer's Rule CalculatorSolve 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.
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Matrix Condition Number CalculatorCompute 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.
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Matrix Power (Aⁿ) CalculatorCompute 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.
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Matrix Norm CalculatorCompute 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).
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Inverse Matrix CalculatorFind 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.
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Matrix Trace CalculatorCalculate 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.
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Matrix Addition and Subtraction CalculatorAdd 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.
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Matrix Multiplication CalculatorMultiply 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.
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Matrix by Scalar CalculatorMultiply a 2×2 matrix by a scalar instantly. Enter your scalar and matrix entries to compute cA element-by-element with this free calculator.
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Hadamard Product CalculatorCompute the Hadamard (element-wise) product of two matrices. Enter dimensions and values to get A∘B where each entry is A_ij × B_ij.
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Quaternion CalculatorFree quaternion calculator: compute the Hamilton product q1×q2, the norm (magnitude), and the conjugate of two 4-component quaternions instantly.
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n×n Matrix Determinant CalculatorCompute 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.
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Angle Between Two Vectors CalculatorFind 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.
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2x2 Matrix Inverse CalculatorCompute 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.
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2x2 Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Handles real and complex conjugate eigenvalues using the trace and determinant formula.
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2×2 Matrix Multiplication CalculatorMultiply 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.
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Adjoint Matrix (Hermitian Conjugate / Conjugate Transpose) CalculatorCompute the adjoint matrix A* (Hermitian conjugate / conjugate transpose) of any real or complex m x n matrix. Transpose then conjugate, with worked example.
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Adding & Subtracting Vectors CalculatorAdd or subtract two 2D vectors to find the resultant magnitude and direction (angle). Computes Rx, Ry, magnitude √(Rx²+Ry²) and θ via atan2.
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3x3 Matrix Determinant CalculatorCalculate the determinant of a 3x3 matrix and its reciprocal (1/det A) using cofactor expansion. Enter nine real entries; detects singular matrices.
