Matrices, vectors, and linear systems
Find the characteristic polynomial p(λ) = det(A − λI) of any 2×2, 3×3, or 4×4 matrix. Get every coefficient, the trace and…
Compute the determinant of any 2×2, 3×3, or 4×4 square matrix with a full step-by-step cofactor (Laplace) expansion. See…
Generate RSA public and private keys from two primes, compute the modulus n and Euler totient φ(n), pick a valid public exponent…
Find the column space of any matrix from 2×2 up to 5×5. Get a basis for Col(A) from the pivot columns, the dimension (rank),…
Compute the singular value decomposition A = UΣVᵀ of any matrix from 2×2 up to 4×4. Get the singular values, the orthogonal…
Compute the Moore-Penrose pseudoinverse A⁺ of any matrix from 2×2 up to 4×4, even when it is singular or not square. See…
Find the inverse of any 2×2, 3×3, or 4×4 matrix by Gauss-Jordan elimination. Watch the augmented matrix [A|I] turn into [I|A⁻¹]…
Find the adjoint (adjugate) of any 2×2, 3×3, or 4×4 square matrix. See the cofactor of every entry, the transpose that flips…
Find the cofactor matrix of any 2×2, 3×3, or 4×4 square matrix. See the checkerboard sign pattern, every first minor, and…
Add or subtract two matrices from 1×1 up to 4×4 and see every cell worked out one at a time. Because adding matrices is possible…
Raise any 2×2, 3×3 or 4×4 square matrix to any whole power from −40 to 40. See how to square a matrix, watch the full exponentiation-by-squaring…
Multiply two matrices from 1×1 up to 4×4 and see every entry expanded as a row-by-column dot product. Get the product A ·…
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