Matrix computation
A matrix computation ledger: 17 operations — from RREF and determinant to eigenvalues, eAt, LU/Cholesky/QR, least squares and SVD — carried out in exact rational arithmetic (BigInt fractions, extended to quadratic fields ℚ(√d)). Every step is annotated as in a notebook; the theorems used appear with statement and proof, and the result is certified at runtime with independent checks in exact arithmetic. Note: the generated content (steps, theorems, proofs) is produced in Italian by the engine.Allowed cell values: integers, fractions and decimals (converted to exact fractions): no rounding error, ever. Empty cells count as 0.
Problem
A =
Allowed values: integers
3, fractions -4/7, decimals 0.25 (converted to exact fractions). Empty cells = 0.Statements and proofs
Why the algorithm is correct
Keywords: matrices, matrix computation, determinant, eigenvalues, RREF, LU factorization, Cholesky, QR, SVD, least squares, exact arithmetic